A recursion equation for prime numbers

2007/11/26 by Keller, Joseph B. · 1 citation
#11A41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0711.3940

Abstract

It is shown that the first n prime numbers p₁,...,p_n determine the next one by the recursion equation p_n+1 =lim_{s→ +∞} [∏ⁿ_k=1 (1-(1)/(p^s_k)) ∑^∞_j=1 (1)/(j^s) -1]^-1/s. The upper limit on the sum can be replaced by 2p_n -1, and the result still holds.

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