Cramer's conjecture
From Polymath Wiki
Cramer's conjecture asserts that the largest gap between adjacent primes of size N should be [math]\displaystyle{ O(\log^2 N) }[/math]. This is compatible with Cramer's random model for the primes, and specifically with the belief that the number of primes in [math]\displaystyle{ [n,n+\log n] }[/math] should resemble a Poisson distribution asymptotically.
If this conjecture is true, one has an easy positive answer to the finding primes project in the strongest form; one simply searches an interval of the form [math]\displaystyle{ [N, N+O(\log^2 N)] }[/math] for primes, where N is your favourite k-digit number.
