# Polignac's Conjecture

**Conjecture**Polignac's Conjecture: For any positive even number n, there are infinitely many prime gaps of size n. In other words: There are infinitely many cases of two consecutive prime numbers with difference n.

In particular, this implies:

**Conjecture**Twin Prime Conjecture: There are an infinite number of twin primes.

## Bibliography

*[P] A. de Polignac, Six propositions arithmologiques déduites de crible d'Ératosthène. Nouv. Ann. Math. 8 (1849), pp. 423--429.

* indicates original appearance(s) of problem.

### Flaw

On January 13th, 2011 Hugh Barker says:

OK, someone has spotted the inevitable flaw in the logic and pointed it out, so not worth looking after all (though feel free if you want to play "spot the error"...

### Compressed version

On January 11th, 2011 Anonymous says:

There's a slightly compressed version of this proof here:

http://barkerhugh.blogspot.com/2011/01/twin-prime-proof-compressed-version.html

Probably better to refer to this one as it is more focused.

## Link

I removed this link and its description from the problem, since it is now known to be incorrect. For future reference here it is: http://barkerhugh.blogspot.com/2011/01/twin-primes-and-polignac-conjecture.html