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Prime number

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A prime number is a natural, whole number that has exactly two distinct whole numbers that divide it with no remainder. These divisors are the number itself and 1. in other word prime number is a numbr that have 2 factors.

For example, 7 is a prime number, because the only numbers that divide it evenly are 1 and 7. 91 is not prime because 1, 7, 13, and 91 all divide it. 1 is not a prime number, since there is only one number that divides it with no leftover.

All natural numbers except 1 that are not prime are called composite numbers.

There is no biggest prime number, as there are infinitely many prime numbers. The way they are placed among all whole numbers is not understood very well, although mathematicians have some understanding of it. See the Prime number theorem.

How to find small prime numbers

There is a simple method to find a list of prime numbers. It was created by Eratosthenes, and has the name Sieve of Eratosthenes, because it catches some numbers that are not prime (like a sieve) and the rest of them that can get through are prime:

  • On a sheet of paper, write all the whole numbers from 2 up to the number being tested. Do not write down the number 1, because it is not a prime number. 1 is not prime because it can be divided only by itself, and not by two different numbers.
  • At the start, all numbers are not crossed out.

The method is always the same:

  1. Start with 2.
  2. 2 is the first number on the sheet (one is not prime), so it must be prime.
  3. Cross out all multiples of the last prime number that was found. All numbers crossed out are composites (not prime), and do not need to be checked any further.
    The first time (2), cross out numbers 4, 6, 8, and so on. The second time (3), cross out numbers 6, 9, 12, and so on.
  4. Go back to the start of the list. The first number that is not crossed out is a prime number.
  5. Go on checking until there are no more numbers on the list. The numbers not crossed out are the prime numbers.



What prime numbers are used for

Prime numbers are very important in mathematics and computer science. Some real-world uses are given below. Very big prime numbers are hard to find, so most of the time, numbers that are probably prime are used.[source?]
