11

Answers
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5
Asymptotic bounds on $\pi^{-1}(x)$ (inverse prime counting function)
6
Are sums of the inverses of prime siblings finite?
4
Square and reversed integer
2
A divergent series related to the number of divisors of of p-1
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Integer dynamics hitting infinitely many primes
8
How can an integer be factorized as n*m so that n^m has the highest value.
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Mathematicians whose works were criticized by contemporaries but became widely accepted later
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Sum involving binomial coefficients
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Not especially famous, long-open problems which anyone can understand
5
Upper bounds for the sum of primes <= n
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Why Mertens could not prove the prime number theorem?