Erdős Problems

Tags Prizes

OPEN

Let $c_1,c_2>0$. Is it true that, for any sufficiently large $x$, there exist more than $c_1\log x$ many consecutive primes $\leq x$ such that the difference between any two is $>c_2$?

#238: [Er55c]

number theory, primes

This is well-known if $c_1$ is sufficiently small.