Is This Formula for Generating Primes New?

[Loren Booda]

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

$$\prod_{n=1}^Np_n-1=p_Z$$

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.

 

[ramsey2879]

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

$$\prod_{n=1}^Np_n-1=p_Z$$

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.

The above formula has been used to prove that there are an infinite number of primes and is well known. Unfortunately I believe the larger n is the less chance that the number is prime even though it is clear that all primes up through the Nth prime do not divide this number.

 

[Borek]

2*3*5*7*11*17-1 = 107*367

(you are not the first one with this idea )

 

[CRGreathouse]

See http://www.research.att.com/~njas/sequences/A005265 and related sequences.