There are infinitely many primes 
which divide some value of the partition
function P.
Erdős-Ivić Conjecture
See also
Newman's Conjecture, Partition Function PExplore with Wolfram|Alpha
References
Erdős, P. and Ivić, A. "The Distribution of Certain Arithmetical Functions at Consecutive Integers." In Proc. Budapest Conf. Number Th., Coll. Math. Soc. J. Bolyai 51, 45-91, 1989.Ono, K. "Distribution of the Partition Functions Modulo
." Ann. Math. 151, 293-307, 2000.Referenced on Wolfram|Alpha
Erdős-Ivić ConjectureCite this as:
Weisstein, Eric W. "Erdős-Ivić Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Erdos-IvicConjecture.html