Problem

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

Tags: number theory, prime numbers



Let $p_1,p_2,\dots ,p_n$ be all prime numbers lesser than $2^{100}$. Prove that $\frac{1}{p_1} +\frac{1}{p_2} +\dots +\frac{1}{p_n} <10$.