Vinogradov's theorem established a very large lower bound on a statement about an operation involving these objects, which Harald Helfgott recently claimed to have reduced drastically.
Vinogradov's theorem established a very large lower bound on a statement about an operation involving these objects, which Harald Helfgott recently claimed to have reduced drastically. Euler proved that the sum of reciprocals of them less than n grows roughly as the log of log of n. Legendre's conjecture asserts that one of these objects always exists in a certain range. If for all numbers a less than n, a to the power of n minus one equals 1 modulo n, then n is either a (*) Carmichael number or a number with this property, as a result of Fermat's Little Theorem. A function counting these numbers grows as x over natural log of x, according to a result due in part to Hadamard. Ben Green and Terence Tao proved that there are arbitrarily long arithmetic sequences in which each term has this property. For 10 points, identify these numbers which have precisely two divisors: one and themselves.
Vinogradov's theorem established a very large lower bound on a statement about an operation involving these objects, which Harald Helfgott recently claimed to have reduced drastically.
prime numbers [or primality]