Simon Plouffe has found a formula which produces 50 prime numbers in a row:

\begin{align} a_0 &= 10^{500}+961 \\ a_{n+1} &= a_n^{\frac{101}{100}} \end{align}

$\lfloor a_n \rfloor$ is a prime for the first 50 $a_n$!

He's trying to find better formulas than those discovered by Wright and Mills, which produce infinitely many primes but grow really quickly.

Paper on the arXiv: arxiv.org/abs/1901.01849

(thanks @erou)

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