Prime Numbers Formula: 1800s Math Discovery

[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?

 

[Office_Shredder]

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

 

[DeadWolfe]

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

 

[Office_Shredder]

http://www.jstor.org/view/07468342/di020779/02p0348s/0

This site seems to have good information

 

[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!

 

[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.

 

[StatusX]

But if you look closely you'll see that it's cheating you...

Could you explain this?