# A prime generator I discovered

1. May 13, 2009

### 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 pZ than Mersenne in a given interval, but requires knowledge of all primes to pN, the Nth prime. It may produce only primes, rather than Mersenne's hit-or-miss search. The pn here are supposed to follow 2, 3, 5, 7, 11, 13, 17...pN, 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.

2. May 13, 2009

### ramsey2879

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.

3. May 13, 2009

### Staff: Mentor

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

(you are not the first one with this idea )

4. May 13, 2009

### CRGreathouse

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

Last edited by a moderator: May 4, 2017