# Prime number formula

1. Apr 28, 2007

### Universe_Man

I was told by a math teacher I met recently that there is a formula that a mathematician in the 1800's came up with that accurately predicted all of the primes up to a certain point, but after that point began to miss a few primes, and after awhile, wasn't useful at all. Does anyone have any information on that?

2. Apr 28, 2007

### Office_Shredder

Staff Emeritus
There is a polynomial in N that gives primes for something like n=1 through 79, but then falls apart. I can't remember what it is at the moment, but I'll try to find it if nobody else posts anything

3. Apr 28, 2007

For some reason I'm recalling that it actually appears in Wittgenstein's Philosophical Investigations, but I'm not sure if that's right...

4. Apr 29, 2007

### Office_Shredder

Staff Emeritus
5. Apr 29, 2007

### Data

You can, of course, construct polynomials that will give you all the primes up to any arbitrary point, if you already know what they are!

6. Apr 29, 2007

### Dragonfall

The positive solutions to the following system of equations are precisely the primes. But if you look closely you'll see that it's cheating you...

0 = wz + h + j − q
0 = (gk + 2g + k + 1)(h + j) + h − z
0 = 16(k + 1)3(k + 2)(n + 1)2 + 1 − f2
0 = 2n + p + q + z − e
0 = e3(e + 2)(a + 1)2 + 1 − o2
0 = (a2 − 1)y2 + 1 − x2
0 = 16r2y4(a2 − 1) + 1 − u2
0 = n + l + v − y
0 = (a2 − 1)l2 + 1 − m2
0 = ai + k + 1 − l − i
0 = ((a + u2(u2 − a))2 − 1)(n + 4dy)2 + 1 − (x + cu)2
0 = p + l(a − n − 1) + b(2an + 2a − n2 − 2n − 2) − m
0 = q + y(a − p − 1) + s(2ap + 2p − p2 − 2p − 2) − x
0 = z + pl(a − p) + t(2ap − p2 − 1) − pm.

7. Apr 29, 2007

### StatusX

Could you explain this?