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Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.

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Number of prime factors in the pronic series used in Saidak's proof?

Saidak's proof on infintely many primes defines this recursive series: $n_{i+1}=n_{i}*(n_{i}+1)$. If $n_1=2$, we get 2, 6, 42, 1806, 3263442 etc. The number of prime factors in this series is 1, 2, 3, …