OEIS A000041 #1

[rwst]

What is the conjecture

For any prime $q$ there exists a partition number $p(k)$ such that all primes $p \le q$ are factors of one or more $p(n) <= p(k)$.

See https://oeis.org/A000041.

Prerequisites needed

Status: open

Choose either option

• I plan on adding this conjecture to the repository
• This issue is up for grabs: I would like to see this conjecture added by somebody else

[aviralgarg05]

I would like to solve the issue. Please assign me the issue

[aviralgarg05]

Please assign me this issue

[rwst]

I'm on it, sorry.

[rwst]

This is the same as "for every prime there is a partition number divisible by it" which was proven by Ken Ono (2000), see https://arxiv.org/abs/math/0008140