Yo, he's kind of spittin' though. Why he's kind of spittin' though? How's it going everybody? Dato Nui here, back again with another Dragon Ball Fighters ranked match video. This time we are using a team of Napa, Krillin, and Yamcha, just because they're such a good assist to Napa, and I really wanted to use the character. Our opponent by the way is heavily themed around Gojira. He had the name tag, everything. I think it'll show it in the game, but Napa, power up. Talk to him, Napa. There's got to be a reason we're able to breathe here out in space about time and give you a proper greeting. A Saiyan hello. I'm down. Also they're playing Kefla and Android 21, so this is this is already terrifying. I'm gonna go for an early Dragon Rush so I can set the stage up. It's always nice to go for an early one because now he's thinking about that for the rest of the game. All right, I'm gonna go for a quick bean plant. Oh, don't try to hit me. Simon, just get this man. Yeah, Simon. Yeah. Also, just so nobody makes the joke in the comment section, it was on purpose that I dressed them both my assistant green. You know, I gotta set the stage for the boys, make sure that they look like Cybermen, don't want Napa attacking them.  That's a joke. That's a joke. I just, I always want to preface this statement so nobody, I don't want any Napa players to be like, oh my goodness, 30% damage, let's go. I gotta get my guys in green. Nah, we're just gonna, what did I have for these? Oh, what is this stuff? You know what? I think you stole that from Krillin, that move from Krillin. I don't know who you got that from, whether it was Napa or, no, it had to be Krillin, but you used Solar Flare better than I will in this set, so that was amazing. All right, gonna go for a somewhat early game, Spark. No, no, dude, that was, but you know, I had it in the back dash. That was unfortunate. I just wanted to, do I have a jump? I do, okay, nice. Yo, he's kind of spittin' though. Why he's kind of spittin'? 6M? Oh, I tried to armor through that. Oh, the keyblasts are gonna be a danger.  I really love, Napa is what I think Raditz would kind of somewhat play like, maybe not as like big in hulking, but definitely like the big Saiyan armor, dude, like the imposing gameplay. I want that, but for Raditz, where's Raditz at, Arksis? He's gotta be somewhere. Ain't that? Let's go. Oh, nice finish. It could have been, it could have been great. Oh, no, please don't tell me you got Yamcha, too. OK, well, at least, yeah, at least Napa's going to die before we can get to the super portion of that, but obviously not a great play on my part. We're going to go for a beam assist start. I feel like that start up took too long for me. I don't think I did that fast enough. Have to look good with the assist, the sea assist, of course. Gonna stretch this for all the damage it's worth and then go into a level three. Um, OK, two beams and two solar flares. Not impossible. I got to watch out for any command grabs. Oh, I didn't think that would connect, but the beam does. That should be death. You do not want to get hit by a beam from Krillin. Look at all of this damage just adding up. All right, I think I need to make this a three bar. Yeah, it's better to be safe than sorry. Better to be safe than sorry. I learned that the hard way in multiple games. Now we're just down to Kefla here and we just got to hope we can put this away down. Oh, no, oh, barely. That barely got me out of that spot and I've still messed it up. It's going to be tough. It's going to get just Krillin and Kefla now. I don't know why I said TN. I was thinking of the tournament tournament of power. I still can't believe they did TN like that. Level one. Is that going to be enough? It is. Oh, just barely. Just barely. Oh, at that point, I wish he lived. All right. Come at me, Kefla. Come at me. No, I can't believe I went with the heavy there. It was too slow, but I was still recovering. I whipped it and I was still recovering. And that's when he hit me with the light. All right. Game one goes to the Kefla. I was going to say Gojita, but I think Gojita got taken out pretty early by the Cybermen. Dude, let me get some more Cybermen strats running. That's how we're going to win these games. Big Cybermen plays. Clap this man. Okay. I was worried I was going to drop that. Boom. I tried it though. He really did try that one. That is crazy. Oh, talk to him, Cybermen. Oh, talk to him, Cybermen. Talk to him. Why don't I talk to him from here on out? Why don't I talk to him? I'll talk to him for the rest of the time. Oh, that is kind of wild in this game. His C assist ain't the best, though. I think I need to pick a different assist. Is C assist that good for Nappa? I just kind of use it because I don't know what else I would want. But maybe I should go back to the A assist. The A assist wasn't bad, per se. But, you know, I just wanted to try out some other stuff. Oh, my God, are we swinging at nothing? Who would say? I didn't even know Yoncha had that voice live. Oh, barely. And we cannot count on that move to hit from that distance. I have to be a bit more reserved when it comes to that. Dragon rush again. Let's go. We got to start moving. Corner. So we're just going to go with this, obviously. Why do I jump? I don't know why I do that. I put myself in the corner. I got hit with a 2M. We're probably dead. Yeah, it's looking a bit dangerous in terms of health. Hopefully we can squeeze out. I mean, it doesn't matter. Actually, whoa, whoa, was that? I don't, was that necessary? I think that was necessary, actually. That still sucks, though. Android 21 got away with a lot of blue life. But we still have the most important assist for Nappa. And that is the beam assist.  Oh, no. My air and airs are also sucking. Where this Kefl is just amazing. All right, I'm going to go for the switch out here. Got the Sidemen on back duty. You're going to be spitting for a little while. Ooh! Get him, Sidemen! Get him, no! Don't leave me, Sidemen! Come back! All right, what is the mix? I have to pose the greatest question, don't man. What is the mix? Oh, no. That was supposed to just be a simple spark. I'll take it. That should be death. Yeah, I'm just going to. OK, OK. It was a blue combo, and we dropped it, and we also vanished. I just panicked. I don't know why I forgot Nappa does not have a standard down heavy. I literally just blanked. Yeah, I deserve that one. I don't even know why. Super dash, to be honest. Is that going to be able to kill with three bars, though? I don't know. It's actually going to be questionable, especially with sparking healing. It does not look like it. But most of the damage is in the beam. And the answer is, though it was not enough, oh, probably should have just taken my lumps with Nappa. Probably should have just let Nappa get the brunt of that one. But we're back out. And you know what? I'm going to change fate. I'm going to change history. Oh, why did it? Why did it give me that one? Did I hold it? Doesn't matter. That actually connected. No, that armor move takes a while. Also, the poor Cyberman, dude. I've taken out well before his time. We're going to play slow here. Oh my goodness. Yep. Yeah. OK. Don't want to over commit to anything. I'm also very afraid. Sparking Kefla is very scary. Oh, no, I overcommitted right there. Oh, I'm getting so close to death so many times. It's death. Oh, barely. If that didn't work like that, we would have died. But the table, the script has been flipped. We come out on top with a win. But that was a very bad beam. I really wish I wasn't rewarded for that. But I was. And you know what? I'm going to take it. I hate the Krillin, the object of different shades of green. I wish that I wish color four was just like standard across the board, like this is what green you're getting. But no, it does not work like that. You G to actually going to start off with a combo and after this time, that's unfortunate. Usually like to start off strong with these kind of things. Well, to age, I'm going to have to spark for that. Got him. Try not to make this spark a waste. Maybe I don't want to get caught by any DPs. I love this character. I love this character. Just start saucin' on him with the side, but what? I really got a main nap on one of these days. I'm just a nap of main. I'm a nap of main in the wings, dude. I'm just when the Napa community calls, I'm here to answer. I don't know why they would ever call. But you know, if you guys need me, if we're playing, if you guys are like doing a pickup game of fighters, I'm right here, dude. Pick me last. I don't think you can kill here. But this is going to give him three extra moves on his bar. You can watch him fill up bottom left. A lot of yellow moves there. Dragon rush genius. I didn't expect it, unfortunately, that we unfortunately that we lost another character that early after gaining the lead like that, especially because we did you spark.  It's not like we had a big lead going on there. Another big hit Krillin just getting taken for a ride. See, we have the worst part about this. I have seven bars that are just sitting there, dude.  I'm going to get expensive. Let me get expensive in my movement real fast. I'm going to do it again. If I do it once, I got to do it twice. Why do I keep putting myself in that corner? Stop that, get some help. Nice super dash. 2S was a risky move to use there, I guess. Believe it, a blue move. Solar flare is now in the pocket. So he has an air solar flare. We got to remember that. Can't use it on the ground, but can go for it in the air. I want to switch, but I also really don't want to get the object hit. Probably should have raw tagged. Yikes, dude. I don't know if this comeback's looking possible right now. Android 21 is such a problem character for me and I just didn't block. Try to get the medium. Stop this 21. I need you to stop. I need you to stop. That's what I mean by the air. Oh my goodness. There we go. That's what I was fishing for. I was trying to make it so I could vanish level one, but I still think I still have to look. Save bar, definitely not a drop, but just saving bar. Okay, that was awful. I was trying to get it so a one bar would kill, but I should have probably threw an EX on there if I wanted to make that happen. Woo, let's go. Perfect. Lot of damage at a level three. Oh, now we set up a nice sparking ring. This is a Yamcha flow chart. So if he sparks, we get damage off this. He saved it. I should have 2M. Oh baby, we're still playing Yamcha though. Oh baby, it's a Yamcha flow chart. Oh babe. Okay, round three, here we come. Around, I guess technically round four. If we win it though, that is three wins and we can get out of here. Let's see if it's possible. Let's see if Napa can bring it home. That game, it did come down to one of his assignment helpers. All right, keep your eyes open. Keep your eyes on the ball. Goes for the one knee into a low. Goes for one knee into a standup. 6M on that one, overhead. I didn't block all 15 hits of his overhead. His jumping medium, that's on me. Probably should have blocked all of them. That jumping medium is an amazing button. I feel like if Gogeta got like a couple buffs to some of his lights, man, I would hate to. I would hate to see a top tier Gogeta, dude. That would be awful. It would be not a fun time for me and my defensive skills. Also, we lost now. So it did not come down to Napa. It did not, absolutely. This game, Napa had no effect. Hopefully, my other characters bring the heat.  Oh, barely enough time. That was basically a Gogeta exclusive. If he wasn't Gogeta, we would have been dead. Dragon rush. It's not even really that great of an option with Gogeta because it takes so long for that light to wrap up. A lot of people forget you can still go behind after that. Okay, back up, back up. Oh, what was that interaction? Let's go. Still going behind the back. Hold on, this is for Napa. We're doing this for him. Am I a genius? Did I mean to do that? No, I didn't know he was gonna tag. You know, I was playing very aggressive. I probably should have expected something along the lines of a reflect. Pack it up, pack it up, Yancha. Don't get too aggressive. Don't get too aggressive now. Let's not overextend the boundaries. Oh, I'm still doing it though. I gotta remember that wake up reflect. Just gotta give him some room to breathe. Gotta look out for that option. Okay, so Yancha died for that, unfortunately. That was a costly mistake. All right, Krillin was sparking though. So not all hope is lost and also there's a lot of Dragon Balls. Oh, I shouldn't have brought it up, Shenron. I shouldn't have brought, I won't bring it up again. I won't bring it up again. Do you have my word? Do you have my word? I'm going for the Dragon Balls. Everybody here knows I'm going for it. I might as well speak the truth, dude. Well, how to throw away all of your options of winning in one easy step by me. I think I'm gonna look to be publishing that book, trying to make it a New York Times bestseller because I just gave up every option. I didn't know what I wanted. Okay, well, it sucks because if I chose either option, I think I would be in a great position to win right now. Move is sick. Okay, okay, shouldn't have used a beam against Kefla. That was my be. Don't level three. Don't level three, don't level three. Don't level three, I'm not trying to block. Okay, my defense is being questioned right now. Are you really questioning my defense? My iron defense, dude.  I'm cracked, I'm cracked. My turn. Okay, your turn, your turn. My iron defense is starting to show its age. It's all rusted. Okay, two to two. It is two to two right now. And that sucked. Hopefully you guys have been enjoying this video though. If you have, definitely go down below. Let me know in the comments and hit the like button. And thank you guys so much for the support on the channel recently. Hold on guys, hold on. But yeah, hit the like button and subscribe if you haven't enjoyed the video. No. All right, we got to set our feet. I'm trying to get more Simon. That's the main problem. The Simon ratio has been all off, dude. In the games I've lost, there's been less Simon. So we need more Simon. Am I gonna really spark to get more Simon? I think we can all say the answers, yes. What, what, what even what? No, I should have used the beam assist. I did plant one though. I did plant one, right? Simon, help. If you can hear me. Okay, I don't think the Simon was there. I'm gonna go for a level three. I don't know what else to do. I don't know what else to do. EP, that was smart. Through the key blast. I think that's it. I think we're goners. Oh no. Leave it. Yeah, yeah, he didn't drop that? I thought that dropped for sure. Okay, okay, that was sick. I'll give it up. He still has spark. If he gives us too much of a frame, oh, I was definitely trying to vanish. I was definitely looking for a cheeky vanish just out of one of his attacks. Can't you see I'm fighting Gojita right now? Kevlar, that was very rude. Okay, we are behind now. We are fighting from behind. Don't guard cancel, just block, just block. All right, we're out, we're out, we're out. We are good to go. The question is, do I wanna, I think I do, right, we have to switch out. We gotta save both of our assists if we're gonna make this come back. We gotta, if we're down a character, we can't lose another one, dude. So let's just keep it, let's keep our cool. Yeah, let's keep the cool, let's keep it cool. No need to rush these things. No need to rush. Two, two, okay, it's two, two. Two characters left on each side and Gojita's even a little weaker. The main thing holding me back from getting excited is that sparking. I gotta stop attacking this 21. Really, no reflect that time. Oh, I should have gone for the 2M. Oh, don't, I don't wanna see it clash. Counted a little too much on the beam. All right, now that I'm looking at, I'm like actually going looking for this reflect. Not seeing a lot of reflect.  Kevlar's holding down, let's go. Oh, nice blocks.  The more health we lose, the longer that sparking is gonna be to hold out. Command grab, that's death if he wants it to be. He's extending it. Oh, no drops. Well, it's gotta be another level one, so at least Gojita does come out. So if we kill Gojita, is that a one touch on Gojita? Yeah, it should be. Three bars, if we get a decent enough touch on Gojita, it's one touch. Why'd I go for the heavy? Stop going for the long heavy. It takes too long to recover. Let's go for a medium. I didn't block, are you kidding me? I missed the block. Oh, no, drop it, drop it, drop it. Hope for a drop, hope for a drop, hope for a drop. Hope for a drop. Oh, heartbreaker of a game.   Well, that is going to be the video. Hopefully you all enjoyed it. Great games to my opponent. And of course, thank you guys so much for watching as well. I can't just thank the opponent. But while you're here, let me know your favorite moment down below in the comment section. And while you're down there, make sure to like button and subscribe, and check out some of the other videos that should be up on your screen right now. Other than that, I've been Dr. Doya, of course. And thank you so much for watching this video once again, all the way to the end. And I will see you in the next one.


t all worked out and that you're all right Yes, in the wake of what about Uh, there might be a lot of reading from chat, but I'm interested to see you guys break down winter soldier Oh, we did and um yeah, because the The nature of copyright, uh, because it was just constantly trying to show shit from it. It was like Probably best To to do it with the the format of um, I think I had vegas open actually that's how I was doing it Um Yeah, it went over great everyone was very happy with our coverage and agreed Nothing horribly controversial in terms of the entire comment section saying you're insane happened. Okay. It's totally fine It wasn't even I think people were that annoyed at critic being critical of winter soldier It was the notion that far from it was better That was a upset and a lot of people that was a controversial one, but yeah Um, hello all more importantly high rags Hello, I'm a blazing bisexual myself, but have trouble asking females out any tips would be appreciated Asking them out. It's very female specific Shall we say? um tips um I don't know.  It sort of sorts itself out, but Yeah It's things to say it's it's so specific to the person. It's just so specific to the person um Things to say that Yeah, I don't know if I can help you there. Just be a good maybe the key isn't what to say but Just displaying that you can listen and you can ask questions and Oh, yeah, if you're gonna say things say questions bitches love questions Especially if they relate to things that she has specifically talked about or has just mentioned You know, it don't like fake interest in a malicious way But people you know show that you have an interest in the things that she says and so ask questions based around that or Um, even if it doesn't necessarily need clarification, maybe every once in a while ask for clarification so that she You know, she knows that you are paying attention. You know things things of that nature Oh, there you go Um, ask meme the christmas vs halloween question already. I assume we did. I don't know what he said though Random but in lord the rings fellowship. Why wouldn't saruman kill gandalf in their first fight to saruman? No, he could come back also high ragsy poo. No, he wants him to join The um, he does indeed impels him on the top of the tower That uh Yeah to join him But he won't because he's gandalf I love the lion gandalf gives him before leaving the uh, there's only one lord of the rings and he does not share power Cool Hey, ifap crew. Hello Hey Hello Mola, hope you enjoyed the new moopa comic I made no more no more. Oh, I remember the no more one. It's based on the uh, the The reading we were doing with jay longbone Remember there's there's some old dude in a bed going no more Yes, I do. I do remember that stuff Uh, watching invincible and at about episode five and six they introduce a broken power and a dumb character choice That essentially dooms the show so disappointed Oh man Yeah, I think this will probably encourage like new super chests to be like, you know, the guy's saying that about invincible Right Who knows Uh, have any of you read the final chapter of attack on titan? If so, what did you think about it? You know, I said no from all of us, right not read it Yeah, I'm afraid we're out of the loop on that one I heard it went through a bit of a flume controversy in relation to story choices But I kind of remember if that was the show or the manga that's getting that criticism And just right made a video that was from what I gather insane and then he deleted it Uh related to like Attack on titan being pro fascist or something. Yeah Yeah, some weird political video he took down. I remember dev was talking about how it was nuts Yeah, uh, his audience were not happy with that one It's um, yeah, I don't know. It's just when you you make things fit and if they don't sort of thing Yeah Um Although I don't disagree with it death of the author annoys me because people will use it as an excuse to read A bunch of dumb crap into text to accuse the author of something e.g. Tolkien was racist because orcs are black They can do that and they can be wrong because their references will be shit You can still argue the points with them, but I mean that's that's kind of no getting around death of you Well, even if death of the author wasn't in play people could still So let's take Tolkien for example and all he ever said about allegory was that it exists in my books I ain't telling you what it is. If he says that then we're gonna need more sources, aren't we? Yeah, so like death of the author doesn't stop people from doing those kinds of interpretations Uh, I just I just think that we should knock them down with the references be like so what why orcs black? It's like and then they explain well because And then you're like, yeah, go on They're like, um, you know what actually I don't want to justify this. You're like, yeah, you probably shouldn't should you um negative 5 out of 10 For zilla versus kong the story is watching paint dry and even the monster fighting is not really worth watching Why do people like this movie? Oh, wow. Damn. I've only really heard that it's really dumb fun That's what I tip it's one here. Yeah Oh, I don't know. We'll we'll discover the truth on that eventually in terms of what we're dealing with Is it a fun fun some monster movie or Kind of a king of the monsters where it's like five minutes of monsters and the rest is people being stupid We'll find out Um, you mean kong flue man and the forgotten iron man baddie I I don't uh I don't know what that is No clue forgotten iron man baddie. They're talking about mandarin Are they? I don't know.  That's what I've heard. I didn't even watch it But I've a replacement top gear was also that as far as I know Grand tour however, follow those three up Yeah, you don't want to have to follow them They should have just called it I know they were trying to cash in on the name But you should have just ended it and started something else because we'll just call it that showed us those three What can we do? What can we do? That show just wow was those three Uh, hey moobler. I can't really remember. But what was your stance for your position in the discord? I remember you saying you're more hands-off. Yeah, I don't really have any control over the running of the discord I'm more so a user In a sense. It's kind of like the reddit. It's run by fans because I do not have the time to police a discord So But I obviously I have what is perceived to be the highest rank But I assume because it's just the discord that relates to my work and e-fap's work Rhino cheese Nice, I guess you can make rhino milk. You can get cheese from it. Yeah That makes sense Makes sense to me Um, also finally saw your rampage. Good work.  The one where there's three people working on that one He's getting more nuts thing But then back down to one tfa or and the father.  Yeah, there's plenty of jokes. They come up with that. I You get to feel the need to be like I must tell friends about this Yes It's so offensive. You had to tell your friends Uh, hope the e-fap hosts in chat are doing great today. Oh, that's nice Yeah, me too. Let's hope you're doing great too Uh, why no e-fap league pfps You mean league of legends or someone else legends. I don't know what else I'd be Oh, justice league. Oh I guess because we were satisfied Yeah, because we did we put them on for this night. I got I know that much. Yeah, we did.  I can't remember. I think so I remember Good evening gamers and also high racks Hello I was thinking of making a d&d monster based on the long man when I thought of a fun question What d&d fantasy creature would encapsulate you as a person slash content creator? Isn't flopples This isn't flopples sounds like it could be a d&d monster, but I'm not that familiar with the bestie areas and I am way less familiar than you are I thought I thought the question was gonna ask I I want to put a monster inspired by a long man What you know, tell me about it. What should it have? What should it do? But yeah, I'm not familiar with the bestiary off the top of my head head. That's what it's called my head had to um To to really say unfortunately Um, I've got the books. I just haven't really Poured through them. I haven't pondered them yet. I did some skimming So I could tell you just some things but yeah, I just Can't help you out there. Unfortunately more general questions.  Hi rooglekins bigson Oh, hello Okay Check out northern exposure It's a hidden 90s gem about a doctor contracted to work in a small town in alaska brilliant characters and story I've never heard of it, but I don't know northern exposure Hmm, I have not heard of that. No Uh rags, is it worth it to briefly date a hot but hardcore lefty girl if all I want is her kitty Well, um Is it worth it? You shouldn't deceive people Like that, um If if you are if you are honest with her and you just say I'm just I just want some, you know, a physical relationship I don't want a romantic relationship. Do you want to hook up here and there? That's one thing, but you shouldn't you shouldn't deceive people Also real world lefties and righties are mostly normal people and not like twitter. Yeah, it's uh, Generally all insulated online sort of um You know, yeah, yeah, if you if you find generally in the real world if you find people who are willing to Really go out of their way to antagonize you based on some political position. Then that's a person like that's a That that's like a kind of a good sign. You should stay away from them, you know But yeah, you don't don't deceive people for that purpose just be honest about what you want and um Just say hey, you know, that's it. Uh, you'd be interested in that You and if she's not down for it, she's not down for it And that's that and there are other fish in the sea And that's uh, that's how it is or get on one of those websites. I hear those work out really well Uh, check out Hot Wheels will race and Xceleraces high ragu I didn't know there are Hot Wheels uh Movies or games? I don't even know Hot Wheels games. I don't know if they're Xceleraces sounds like another like brand I guess is it someone who did that one? Yeah, I don't know. Oh no sounds nice though Hello all my n-words keeping the memory of wolf alive and supporting you financially high rags kick jay and watch ronald the barbarian for e-fap movies Ronald the barbarian. Hmm great name for a barbarian. Uh, I know about dave the barbarian Yeah, thank you I'm just says release the e-fap cut which that did happen It indeed. The e-fap vision Even ended up making a video of the snide cut. See the snide cut was just that good that that much coverage was required remember when Flash was like touching some of his hair as they were falling to the death That was weird That was weird.   Like this is a third Obsaid ebbs Fringy do you want to be captain america? And if so, why don't you have any self-respect? Uh Well, do I want to be captain america doesn't doesn't really appeal to me Um, kind of almost doesn't make much sense given that i'm not an american uh I guess captain australia if that but even then I don't know if it appeals to me like to be a superhero Yeah, I mean you got some you got videos to make like you can't be doing superior stuff If I'm doing superhero stuff, then how can I be sitting here staring at this massive timeline? Exactly having to cut all this audio in I mean And mohler thanks for the surprise efapse a day and high rags Hello Did you guys hear that ralf removed his joker video? Yeah, um, I don't know if he's ever put anything out to explain why But we can obviously assume it's because it didn't go over very well. Um It's the worst video he's ever made and that's that's trust me treat that as a nice thing. I'm saying because like I I know he's capable of a lot better than that.  I'll just have the movie stanoch It just just appealing to the meta really more so than anything in the film. Yeah, like how does it ruin the film at all? Uh, is rags rich off dogecoin now? man, this really Yeah, that was a while ago I'm guessing you didn't invest in doge coming back coming back or maybe I did maybe i'm hiding my power level Uh, I got a celery stick in one hand and a glass of orange juice in the other. Let's fap All right. Hmm healthy snacks or yeah, I mean, you know, that's depending what orange juice is what orange juice you've got And uh Yeah, and and and and that about does it for catching up with this as I have dubbed it the justice league super chat catch up Oh, sorry The correct name on that for whatever e-fap it pertains to um But you know, thank you for joining us and um Until next time our journey of catching up on That's I suppose Thanks so much for listening We will be you next time Absolutely


What about that one? A bunny, maybe? I followed Violet's gaze to the misshapen cloud above us. I had to admit, as silly as it felt for our age, cloud-gazing in the unkempt field behind our high school on recess had to be the best part of my day. Hmm, I squinted my eyes towards it and rubbed my chin to relay that I was taking the proposition incredibly seriously. Well, Violet, after my assessment of the cloud, the exact circumference of its frame, the rounding off of what I suppose we could call a tail, I have determined that it is in fact a bunny. She played along with the act, as she always did, and let out a sigh of relief. Just as I suspected, thank you for your time and expertise, Doc, we'll be taking this one to the lab. I smirked. Violet had been my best friend since before I could even put a firm definition behind what friendship truly was. Over the years, she taught it to me through a series of ups and downs, the downs always springing back up with her. We spent our last few minutes of teenage freedom, debating the shape of what I'd like to call a toad before being summoned back to the cold atmosphere I loathed and Violet loved. Attending public school was a treat for Violet. I'd never seen anyone react to cruel clicks or uppity behavior the way that she did. I'd never met anyone who could go on and on about the true wonders of trig until you had to eventually put a stop to it, reminding her that trigonometry was not supposed to be fun. It's fun to me. She'd reply, just a bit offended by the notion that she wasn't a normal child. And truthfully, she wasn't. I remember how scared she'd made me in middle school when only a few years into our budding friendship, she started speaking to me as if there was always someone else around or talking into thin air or pointing and prompting me to look into complete nothingness. Only a short while after this behavior started and teachers began to express concern for her mental health. Her parents pulled her out of public school and began homeschooling her. It wasn't that they were concerned for their daughter. It was that she was tarnishing their name with her oddities. She had what I could only describe as a mental break shortly after that. Her parents didn't believe in therapy or psychiatric help or mental illness and instead forced her into isolation. Even then she'd make it a point to sneak out every night 7pm sharp to meet me in her backyard. I knew it affected her poor 14 year old mind in the worst way and it affected me too. I was too young to understand what was happening to her, too young to help. Thankfully, in the beginning of our sophomore year, Violet's troubles seemed to subside. After a lot of convincing, her parents agreed to allow her back into public school under strict and careful surveillance of course. She loved and appreciated the time away from her home and I loved and appreciated to see her happy. So I suppose I could let her enjoy trigonometry. Her enthusiasm showed in her grades and her parents couldn't argue with that. She'd reached the top of our class by the end of 10th grade and was on her way to becoming valedictorian, all with little to no symptoms of what once was plaguing her mind. I couldn't have been more proud of her. But that day, as we walked back into her sanctuary, she froze in her tracks. I'll never forget the look of terror on her face as she grabbed the sleeve of my shirt, mouth agape, and pointed forward into the crowded hallway at absolutely nothing. Vi, I asked. Nothing. Violet. I shook her shoulder a bit in an attempt to snap her out of whatever trance she was divulged in, but the touch only agitated her. She jerked away from me. Quickly, and the look of terror shifted to the direction of me. After a few moments, she lifted a hand to her cheek, closed her mouth, and then gasped for air. Violet. There was no response from her as she scrambled away from me. I didn't see her anywhere for the rest of the day. And it worried me a lot. The next day, Violet returned, but I could tell that something was bothering her. I tried pressing her to talk to me, but it was to no avail. She was almost unresponsive, like she was only existing to daydream and refused to be disturbed by reality. I chose to allow her that, and I dropped the issue. But when she was nowhere to be found, once recess rolled around, I began to panic. I was already an anxious person by nature, and I cared about Violet. It was unlike her to not make her presence known everywhere she went, and I couldn't help but compare the episode she'd had the day before to her past issues. I was worried that if someone noticed her off-putting behavior, they might notify her parents. I searched everywhere for her until I came to the edge of the land that was owned by our school, indicated by a chain-link fence that separated our world from the woods beyond it. That's when I saw her, or what I could distinguish as her through the brush of it. Her long black hair flowed behind her shoulders and into the trees, as she stood completely still, her back towards me, and her body facing further into the depths of the forbidden area. After a quick glance around to assure that no teacher or rat was sizing me up, I hopped the fence and sprinted in her direction. Violet? Violet, I cried to her. She stayed still all the while until I caught up to her. Why? You can't be out here.  Silence. I placed myself in front of her, looking her dead in the eyes, and realizing she had the exact same expression plastered across her face as the first incident. Terror. Okay, Violet, please, we have to go back. No one can catch us out here, okay? We could get in big trouble for, quickly, and without warning, she lifted a finger to my lips.   I couldn't believe it. Her voice was frantic, and her speech was slurred, but more notably, Violet had never spoken to anyone, much less me, like that in her entire life. She removed her index finger from against my lips and pointed forward deeper into the forest, and cocked her head sideways, before rotating it back up to stare at the sky. Before I had any time to register what was happening, she let out the most heart wrenching, soul piercing scream I'd ever heard from another human being. If it weren't for the fact that I was right beside her, I'd have thought she was being tortured, ripped to shreds, left for dead in a murderous rampage, but here she stood, screaming without pause for breath, proof that she was still here. It didn't take long before an aid found us and rushed Violet inside. Again, she didn't return. The third day was difficult. The normally well put together and carefully orchestrated Violet I knew so well was replaced with a disheveled frantic girl whose eyes darted to any and every sound in the busy hallways of the place she used to love. I was shocked that her parents had even let her leave the house that day, but something told me that she was narrowly avoiding their watch. Trying to speak to her was useless. She wasn't silent as she'd been the day before, but she refused to speak unless spoken to, and when she did speak, her sentences were replaced by a loose jumble of strewn together words and phrases, almost as if she was on complete autopilot and sharing her real thought would steal too much energy from her already exhausted state. By recess, I was begging her just to let me help in any way I could. The offer seemed to strike a match within her as she slowly turned her head in my direction. The first time she looked at me all day. Anything? I nodded without hesitation. I was thinking help in terms of helping her catch up with miss schoolwork concocting a scheme to get around her parents or simply keeping a watchful eye over her while she struggled with something difficult. Violet didn't see it that way. Come recess, she was dragging me by my arm, nearly crushing my wrist towards the forest. Violet, come on, let's not go back there, alright? You remember what happened yesterday? We can't. Anything? She mumbled under her breath as we kept trudging along. She made no effort to dodge anyone's gaze as we marched along as if we were on an important mission that not even God could stop us from completing. I hopped the fence before her as she stared daggers into my back. It was as if I were her only enemy in this world, and I would immediately go back on my word and betray her in whatever problems she was facing alone. I wanted to remind her that I loved her, but I knew it wouldn't matter to her in this state. She pulled me through the woods, twigs smacking her in the legs inside all the way until we got there. The exact same spot she'd been standing in yesterday. I wanted to protest and almost couldn't help myself, but remembered that she didn't care at all to hear it. She seemed adamant about her plan, and I desperately did want to help her. I would have done anything. Slowly, she lifted her finger to point into the forest, a motion I was all too used to at this point, and quickly whipped her head around in my direction. Today, you look. That's when I realized, in all the commotion of the scene she'd caused yesterday, I was too distracted to even attempt to see what she was seeing. I hadn't even bothered. I'd written her off as mental. Today, I would look. Again, she cocked her head sideways and rolled it back. As she stared into the sun, I made a promise with myself and with her to keep my gaze forward, no matter what. She let in a deep breath, and again, she shrieked. At first, I thought there was nothing. I squinted and strained my eyes until I gave myself a headache. But then I saw a tall, dark figure formed among the trees. The thing had to have been standing over 20 feet tall. It towered over everything, the trees, the schoolyard, the forest, us. I couldn't believe that I hadn't seen it until now, that Violet was the only one who'd noticed it up until she'd shared it with me. For a brief moment, I saw what was following my friend, what was standing there, pointing back at her. For a brief moment, I understood her. Before she was once again yanked back to reality by a concerned and frustrated teacher, we exchanged one final look before she was hauled away, a mutual understanding between the two of us that this time she would not be coming back. I rushed to her house after school and was met with something vacant, dark, and unwelcoming. It was obvious that the home was unoccupied, and I feared for the worst. Weeks passed, I stopped at her house daily, but nobody was ever home. The house sat empty, and I kicked myself constantly for not doing more to help her. When it became evident that the family had up and left, I removed every note I'd left her from what was once their mailbox and shoved them all into my school bag. She left without any notice, and I've not seen or heard from her ever since. Violet, if you're out there, I saw it. You're not crazy. You never were.


Everybody's having a blessed day out there. As you can see, we are back here at Troy's Muffler in South Carolina and we got two cars today. We're going to get fixed up. We got Zorro, the new Dodge Challenger RT that we just picked up, and we got Clifford. So Clifford RT is going to get hooked up today with some carnage along with Zorro. All right, Mopar fam. We got Zorro on the rack. About to get that carnage sound. Stay tuned. We're going to do the whole install, welding it up. All the pipes. It's going to be badass. How hard this one going to be? It ain't going to be too bad, but you normally put on the challenges right there. Everybody loves it. I was looking at those or those black ones you got, but I think I'm going to do the black. I'm going to stay with those. It'll work.


So yeah, it's great to be here. My name is Patrick and I'm one of the co-founders of Research Hub and today I'm here to talk about the incentive structure of academic science and how Deciv or decentralized science can help to fix it. So first all a little background about me I've had the privilege of dropping out of not one but two academic science institutions The first was a PhD program in molecular biology at Boston University and the second was medical school at Georgetown There was a common theme between all of my experiences in both basic science research and applied medical research It's that there are centralized Institutions that unintentionally sponsor bad behaviors by creating perverse incentives For instance consider the culture of publisher perish as a scientist It's imperative that you not only publish often, but that your publications generate a lot of citations This is because there are funding bodies who essentially allocate capital based on researchers prior publication history In theory this makes sense right like if you have money and you want to give it to science You want to give it to someone who's demonstrated the ability to do good work in the past But in practice highly cited papers don't always necessarily equate with good work In fact, meta scientists have found that the more often a paper is cited Actually, it's less likely to reproduce in the future and scientists generally don't want to produce like kind of like Incremental small findings because they're less likely to be cited and make them less likely to gain funding in the future The downstream effects of this is a tremendous amount of waste people have estimated that between 50 to 85 percent of all science Is irreproducible, which is essentially just money down the drain and as you can see it's a lot of money So what are we building at research hub to try and fix this We're kind of taking two approaches. The first is to build an online native tool that allows anyone to publish scientific research in the open The second is creating incentives for healthy research behaviors As you can see here We kind of have a Reddit style forum where anyone can earn the ERC 20 token research coin for sharing papers Publishing directly to our forum Openly commenting on these papers and doing peer reviews. We also have some tools that allow for Collaborative writing of scientific papers. This is an electronic lab notebook that allows anyone to work together With their colleagues around the world and publish directly to our forum. It's kind of like a notion editor for science We also have a reference manager. We just shipped which allows scientists to save the papers They're most interested in and then annotate them As you can see here We have one of our immunologists coal who's using our reference manager to leave in line site a or in line comments that become a peer review on research hub calm When you shared content that's been highly uploaded you earn research coin and what can you do with research coin? You can create incentives for other scientists So for instance say you just shared a preprint and you'd like a peer review Rather than paying a journal an article processing charge You can take the research coin you've already earned and create a bounty for another researcher to come in and share a peer review There are lots of ways people are using bounties right now For instance, we have a neuroscientist who is trying a new protocol in their lab They kind of got stuck and they came to research hub to try and get unstuck They created a bounty for an expert to come in and troubleshoot their protocol and they ended up moving forward in their own Experiments in their own PhD career One of the examples that I'm most proud of and I think illustrates what we're trying to do here at research hub is If anybody remembers a couple months ago in Mexican Congress There were aliens that were presented to the world Kind of fortunately the people who presented these aliens actually took a DNA sample and submitted it to NCBI So on research hub we have community members who are interested in this and we're like, hey Let's figure out what's going on here So they got together used our electronic lab notebook and created a post Attached a bounty to it for someone to come in and actually analyze the DNA that was shared on NCBI Spoiler alert unlikely to be aliens unfortunately We had a bioinformaticist within 24 hours of the bounty being created that came in did some analytics and Found that there was a lot of eukaryotic some prokaryotic DNA and some unidentified DNA So yeah, this is kind of like a small example of what can potentially happen at scale with research hub So I want to leave everybody with one of my favorite quotes from Aaron Schwartz the founder of reddit Thank you very much for your time


Hey, what's up everybody? Ricky Karuth here.   And the reason I did is because I was tired of seeing contradictive ads to what I post on my channel, right in front of all my videos.  I'm like, okay, let's see what's running here. Let's see what this guy's talking about. And I just got to the point where, you know, the little three or 4,000 a month I was making on the advertisements just isn't worth it when it comes down to the experience for my subscribers when they're watching my videos. I got completely tired of it. And one day I just said, boom, and I actually thought about this for a while, you know, should I do this? What's it going to do? You know, will my views go down? Will YouTube actually, you know, not share my video with as many people? And hey, that may be true. That's, I hear that that's a big part of the YouTube algorithm. When you watch guys like me, Kevin and Graham Stephan, they talk about this, how you know, they have so many ads running in their videos. And that's one of the reason why YouTube shows it to so many people because they're going to be making money. And YouTube makes money on those ads. And, you know, Graham and meet Kevin and a lot of these other YouTubers make money on the ads, but more importantly, YouTube makes money on the ads. So of course they're going to show more videos that they're going to make money on than not. However, I'm in a different scenario, right? I am really catering to only real estate agents, which let's face it, real estate agents are a very small niche in the whole wide world of the internet. So, you know, for me to, you know, try to make money on ad revenue, big money, it's really just not going to happen in the real estate agent niche. I have to move into a more general niche, personal financing, self development, so on and so forth, and tap into a much larger, larger audience and get to those millions of views to be able to make any real money on YouTube ad revenue. So, like I said, one day I woke up and I decided this isn't really jiving with me. This makes zero sense at this point. And I'm here trying to provide as much value as I can to my subscribers. So, you know what?  And I'm just going to let people see Ricky when they click on a video. And what I have to say. So, moving forward, I'm going to be doing a lot more live videos for you. And it's going to be more breaking news in the real estate industry. I'm going to be sharing, you know, earnings reports of different brokerages. I'm going to be sharing, you know, the statistics, real estate statistics and movements in the market. And I'm really excited about this new chapter for my channel moving forward. I'm going to be concentrating a lot more here. And I really want to go all in with bringing you the most value possible. So, I'm really excited. I want to take this second to thank you for watching my videos. I hope that it's bringing you so much value and helping you take your business to an entirely different level. I've been touring around the country doing live in-person events. And I've been streaming those events live here on YouTube. And, you know, afterwards agents are coming up to me and telling me how much my content has changed their life and transformed their business. And I'll tell you right now that that is the reason why I continue to do this.  And because I'm experiencing that right now, I'm in a place where I'm providing such an incredible life for my wife and daughter that I just couldn't even have dreamed to be in this position. And I just feel so grateful. And I want that for every single one of you. I hope you guys understand that and can feel that when I say it, that I really mean it. And I'm super genuine with my intentions for you. Everything I do is focused around bringing you more value, not me value, not me making money. You know, I'm, I'm winning and I'm going to continue to win. I'm not worried about that. I know how to win. And it all comes from hard work, determination, never quitting, trying to work smarter every day, getting 1% better and never giving up.  And I'm going to continue to push as hard as I can to provide an even better life for my wife and daughter and leave a legacy behind. And I wish all that for you and I'll do everything I could do to help you. So please continue pushing and fighting, you know, to take your business to another level and let me know what I can do to help use me as a resource. I want to be the resource that you reach out to when you have a question, when you have a problem, right? And even when you want to celebrate your wins, continue to reach out to me and let me know when you have those big wins and those aha moments and those questions and concerns. Let me help you through the process and take you to those places that you that you want to get to. All right. Many she's always barking right at the end of my videos, it seems like. So take care, guys. Let me know what I could do to help you. Shoot me a comment. Shoot me a DM on Instagram and let me know and we'll talk to you guys soon. Much love.


This lecture is part of Berkeley Math 115, an introductory undergraduate course on number theory. And today I'll be discussing more on numerical calculation. So the first problem I'm going to look at is the following problem. How do we solve x squared is conglant to minus 1 modulo p? P is a prime and we saw earlier that the prime has a square root of minus 1 if and only if p is conglant to 1 modulo 4 or I guess p equals 2, which is kind of trivial, so we will ignore that. And we saw how to solve this in an earlier lecture. We saw that we can get a solution x is equal to p minus 1 over 2 factorial using Wilson's theorem. So we have the rather curious identity that if you write i for the square root of minus 1, then we find i is equal to p minus 1 over 2 factorial, which looks a bit weird, but whatever. And you might think, well, there we've solved the problem. The trouble is this formula is useless, almost useless. The problem is that if p is large, this takes a lot of effort to calculate directly. If p is a billion, we're going to have to do a billion different multiplications to get this. And this is obviously far too slow for large p. So we want to know, can we find a faster method? So here's an example of a faster method. Let's pick a number b. And I'm not going to tell you how we're going to pick b yet. We'll have to discuss that later. And let's put a equals b to the p minus 1 over 2 modulo p. And you know, this is very fast to calculate because we can work out powers modulo a number very quickly as we saw earlier. And then we notice that a squared is b to the p minus 1, which is plus 1 modulo p. So a is congruent to plus or minus 1 modulo p. That's because the number 1 only has two square roots modulo p because there are no zero divisors. You remember modulo some other numbers, the number 1 can have a rather disturbing large number of square roots. But that problem doesn't arise if p is prime. So if a is equal to minus 1 mod p, then we're done. Because we can now look at b to the p minus 1 over 4 squared is now a, which is equal to minus 1. So we now have a solution b to the p minus 1 over 4 has square minus 1. So all we've got to do is solve a problem. How to choose b so that b to the p minus 1 over 2 is congruent to minus 1 and not plus 1. And there's a very easy way of doing this, which is to guess at random. So you're always told that it's a really bad idea to try and solve a problem by random guessing. But in computational number theory, it's actually quite a good method. The point is each guess has, well, you might say, you know, this number could be either 1 or minus 1. And it's reasonable to assume that it's takes the answer 1 and minus 1 equally often. And we'll see that this is in fact true a bit later. So each guess is approximately a 50% chance to work. So it's it's like tossing a coin and you keep on tossing the coin until heads turns up. And, you know, if you do this, it doesn't take very long to get heads. It takes an average of about two tosses, depending on how biased your coin is. Unless as long as there really is a 50% chance. So so so this gives gives an algorithm to to find a square root of minus 1. You just keep guessing numbers B and working at B to the P minus 1 over 2 until you get minus 1. And then you know B to the P minus 1 over 4 is a solution. It's a bit of a problem to ask how fast is this. And this is a bit tricky because calculating B to P minus 1 over 4 is really fast. This is polynomial time. If we've got B to the P minus 1 over 2, that is just polynomial time in the length of the input. However, the number of guesses might be bounded by a prop about P, maybe P over 2 or something. I mean, turns out that half of all numbers work. So so you only need to check P over 2. But this is going to give you exponential time. So if you're really unlucky with your guesses and just kept on guessing more and more numbers that didn't work, it might take an absurdly long time to calculate this. So the worst case of this algorithm is exponential time. Actually, you can do better than that if you don't guess entirely at random, but that's that's getting rather complicated. However, the average case is just polynomial time. In fact, as I said, the average number of guesses you need to make, if you choose these numbers B at random, is about 2. So the average time is just 2 times polynomial time, which is, of course, just polynomial time. So this sort of problem is quite common in computational number theory. There are actually quite a few probabilistic algorithms which in practice are very fast, but it's kind of difficult to actually prove they're fast because of this probabilistic aspect to them. So let's just see an example of this. Let's solve x squared is congruent to minus 1 modulo 41. So we know 41 is equal to 4 times 10 plus 1. So we pick B and form B to the 10, where 10 is P minus 1 over 4. And if it is plus or minus 1, we have sort of failed because all we've done is we found one of the square roots of 1. If not, it is a square root of minus 1. So we now just start this. What will be, shall we start? Let's just pick B equals 2. We might as well pick the smallest non-trivial one. Obviously, B equals 1 is a bit of a waste of time. That's not going to work. So we work out 2 to the 10 modulo 41. Well, 2 to the 10 is congruent to minus 1 mod 41. So we have failed. We have not managed this. This is not a square root of minus 1. Well, we don't give up. Let's try B equals 3. So 3 to the 10 modulo 41 is congruent to 9. So 9 is a square root of minus 1 mod 41. In fact, even by 9 squared is 81. It's congruent to minus 1 mod 41. So it just took two guesses. By the way, that's what a computer would do. If you were a human, not a computer, you might notice that this step here we could have actually stopped if we wanted. Because this number 10 happens to be even. And we found 2 to the 10 is minus 1. This means 2 to the 5 squared is congruent to minus 1. So in fact, 2 to the 5, which is 32, would give us a square root of minus 1. So if we were really paying attention during this calculation, we could have actually shortened it a bit there. As you will see, this idea turning up a little bit later on in a different context. So another important algorithm is Euclid's algorithm. I'm not going to discuss this because I discussed it in an earlier lecture. So the problem of solving linear equations and finding greatest common divisors has a really fast solution. As I mentioned earlier, there is actually a slightly faster version of Euclid's algorithm that doesn't involve long division, but only division by 2. So it's a sort of Russian peasant form of Euclid algorithm. Instead of doing long division, you just keep dividing by 2. But anyway, what I'm going to do now is some algorithms to test if x is prime. So how can we do this? Well, the first thing is to test all factors less than the square root of x. And the trouble is this is OK for x up to a few hundred by hand, or x up to a few trillion by computer. But it's really pretty slow in general because it takes about root of x steps. And each step we should probably multiply by log of x or something because it takes some time to do this. And this is actually exponential time. You remember exponential time means exponential in the number of digits needed to write x, not in the number x itself. So exponential time algorithms are sort of OK for small input, but not for big input. So what I want to do is to give some examples of faster algorithms. And the simplest one is let's try and write x as a difference of squares. So we're going to write x is equal to a squared minus b squared. And if we can do that, then we've factored x because we can just write this as a minus b times a plus b. And this method was actually used by Fermat to factorise a few numbers. And let's see an example of it. Well, you might say, how are you going to write x as a difference of two squares? Well, you can sometimes do this quite quickly. So let's try x equals 7 3 1 3. And what we do is we pick a square slightly larger than x. So let's have a look. If you try 85 squared is 7 2 2 5. Well, that's a bit small. So we try 86 squared is 7 3 9 6. Well, that's a little bit bigger. But 7 3 9 6 minus 7 3 1 3 is 83. And this is not a square. So that's no good. And then we go to 87 squared. And 87 squared is 7 5 6 9. And now the difference is 7 5 6 9 minus 7 3 1 3 is equal to 256. Now this is now 16 squared. So now we've factorised x. x is equal to 87 plus 16 times 87 minus 16, which is 103 times 71. Well, that sort of worked. But you may be a bit suspicious of this algorithm. You know, it seems to be that we had to be a little bit lucky that this was a square. And you may wonder if I sort of faked this example by choosing something that works easily. And now it says, yes, I did fake it a bit. And the trouble with this method is it sometimes works really well, but it sometimes doesn't. It works best if x is equal to a is equal to 2 numbers a times b with a and b very close. Because if these are very close, then x is equal to a plus b over 2 squared minus a minus b over 2 squared. And if a and b are very close, this will be very small. So this number won't be much bigger than x. And we will hit it fairly quickly by looking at the first few squares. So this sometimes works very quickly, but sometimes doesn't. You may think it works quite well with the first method where we just test all primes up to the square root of x. Because you might say, well, if x is a small prime factor, then we're going to find it with test one. And if both prime factors of x are very big near the square root of x, then we will find it using method two. Unfortunately, for most numbers, they don't want more than one or two very small prime factors. And the other prime factors tend to be rather different from each other. So a typical very large number with hundreds of digits will have one would guess it's going to have one very small prime factor, maybe two, three, or five. And then it will have something with two or three digits. And then it might have something with five digits. And then the next factor might have 10 or 15 digits and so on. So the number of digits in each prime tends to increase quite rapidly. And this method simply doesn't work very well for most numbers because their prime factors are increasing too rapidly. There's one way you can speed this up quite a lot. It turns out there are several congruent conditions that these numbers have to satisfy, as we will see when we discuss quadratic reciprocity later on. So you can, in fact, speed up this method by a factor of many thousands by using various congruent conditions. And this gives some factorization methods called sieving methods, which used to be used quite a bit in the days before digital computers. And people would actually build mechanical sieving devices to factorize numbers. But as I said, that would be easier to discuss later on. So now I want to discuss a bit more about testing if x is prime. Well, we've got this really slow method. You can just test lots of factors of x. And this will work eventually, but it's pretty slow. And we had another faster method. We take a look at a to the m minus 1 and ask, is this congruent to 1 modulo m? And we saw the answer was, if no, this implies m is not prime. And if it's yes, this implies who knows. m is probably prime, but it might be a Carmichael number. For instance, it might be 561. And there are an infinite number of numbers with this funny property. So what I'm going to do now is explain how to have an improved version of this test. So suppose a to the 2n is congruent to 1 modulo m. And if m is prime, this implies that a to the n squared is congruent to 1. So a to the n is congruent to plus or minus 1. So what we can do is, if we've got a to the m minus 1 is congruent to 1, we can look at a to the m minus 1 over 2 and see if that's plus or minus 1. And if it isn't, then m is not prime. And we could even look at a to the m minus 1 over 4 if m happens to be 1 mod 4 and so on. So as an example, let's test the Carmichael number 561 to see if it is prime. And of course, we know it isn't prime. It's divisible by 3 for heaven's sake. But this is just to show you how the method works. So what we do is we take 561 minus 1, which is 560. And we write this as 2 to the 4 times 35. So we take out the highest power of 2 in the number p minus 1. So here we're, I guess we shouldn't call it p because it's not prime in m minus 1. And now we pick a random number, b. And we're going to look at powers of b. And I'm going to take b equals 2 because it's the smallest number. And what we do is we now compute 2 to the 35 modulo 561.  And 2 is our random number b. And we work this out. And we find 2 to the 35 is congruent to, well, let's just compute it using the Russian peasant exponentiation method we compute 2 to the 1, 2 to the 2, 2 to the 4, and so on. And we find these are congruent to 2, 4, 16, 256, 460, and 103 modulo 561. And now you remember, we write 35 in binary as 35 is equal to 2 to the 5 plus 2 plus 1. So 2 to the 35 is congruent to 103 times 4 times 2, which is congruent to 263 modulo 561.  Well, it doesn't tell us anything very much yet. What we now do is we keep squaring this. So we now take 2 to the 35 squared, which is 2 to the 17. Now we just square this. So this is equal to 263 squared, which is congruent to 166. Well, that's still no good. It doesn't tell us anything. So we now work out 2 to the 70 squared, which is congruent to 2 to the 140, which is 166 squared, which, if I've calculated it right, is congruent to 67 mod 561. OK, well, we just keep going. 2 to the 140 squared is now 67 squared, which is actually congruent to 1. So this is 2 to the 280. So 2 to the 560 would be 2 to the 280 squared, which is 1 squared, which is congruent to 1. So since it was a Carmichael number, we already knew that 2 to the 560 was congruent to 1, but we don't actually need this. And now let's look at our calculation. The key point is this bit here. We have found square root of 1 that isn't minus 1. So 67 is square root of 1 not equal to plus 1 or minus 1. Well, this shows that 561 is not a prime, because if a squared is congruent to 1 modulo p for p of prime, then a must be congruent to plus or minus 1. So by doing this refined form of the test, we can sometimes detect that Carmichael numbers are prime. So let's just write out what the test does in general. So to test m to c to c if it's prime, what we do is we put m minus 1 is equal to 2 to the c times d, where d is odd. And now we pick some random number b and we find b to the power of d modulo m. And then we just calculate the squares of this. So we form b to the d squared mod m and b to the d to the 4 mod m until we get up to b to the d times 2 to the c mod m. So this is just b to the m minus 1. And now we take a look at these. And we can see if it's not 1, then the number is not prime. The number m is not prime. So suppose it's 1, then we look at the next one before it. And if it's 1, then we just continue. If it's not plus or minus 1, then this is not prime. Because this number here would be a square root of 1.  So if it's not plus or minus 1, we give up. If it's minus 1, we're stuck. We don't know what the answer is. If it's 1, you continue to the next one and see. So if this one is not plus or minus 1, then the number is not prime. And if it's minus 1, we have to give up. We don't know what the answer is. And if it's 1, you just keep going. So this will quite often work for even four Carmichael numbers and tell you whether the number is prime or not. Of course, it's possible that all these numbers here might be equal to 1, in which case you just can't tell whether the number is prime or not. Or this one might be minus 1 and all the others might be 1 or something like that. So if ever one of these is minus 1, then we're kind of a bit stuck. But that's sort of unlikely. I mean, most of the time, this will tell you that number isn't prime if it's not prime. OK, next, we're going to do some more methods for factorizing numbers. But I'll leave those for the next video.