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## Main Question or Discussion Point

Somewhere between brute force and Mersenne derivation of primes is the formula I found,

[tex]\prod_{n=1}^Np_n-1=p_Z[/tex]

I guess it would generate more primes p

Have I discovered anything new here? The equation is so simple and effective that it must have already been found.

[tex]\prod_{n=1}^Np_n-1=p_Z[/tex]

I guess it would generate more primes p

_{Z}than Mersenne in a given interval, but requires knowledge of all primes to p_{N}, the Nth prime. It may produce*only*primes, rather than Mersenne's hit-or-miss search. The p_{n}here are supposed to follow 2, 3, 5, 7, 11, 13, 17...p_{N}, but the formula might work somewhat with an incomplete sequence of primes.Have I discovered anything new here? The equation is so simple and effective that it must have already been found.