Cramer's conjecture
From Polymath1Wiki
Cramér's conjecture asserts that the largest gap between adjacent primes of size N should be [math]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][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][N, N+O(\log^2 N)][/math] for primes, where N is your favourite k-digit number.
