Cramer's conjecture
From Polymath1Wiki
Cramér's conjecture asserts that the largest gap between adjacent primes of size N should be O(log2N). This is compatible with Cramer's random model for the primes, and specifically with the belief that the number of primes in [n,n + logn] 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 [N,N + O(log2N)] for primes, where N is your favourite k-digit number.
