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M2636

Part of Kvant 2021

Problems(1)

Are there infinitely many simple primes?

Source: Kvant Magazine No. 1 2021 M2636

3/9/2023
We call a natural number pp{} simple if for any natural number kk{} such that 2⩽k⩽p2\leqslant k\leqslant \sqrt{p} the inequality {p/k}⩾0,01\{p/k\}\geqslant 0,01 holds. Is the set of simple prime numbers finite?
Proposed by M. Didin
number theoryKvantprime numbers