Proof of the twin primes conjecture

[StatGuy2000]

I have just found links to a few articles discussing the proof of the twin prime conjecture by Yitang Zhang, a once obscure mathematician working as a lecturer at the University of New Hampshire, and who according to reports had difficulty finding academic work and worked as an accountant and a Subway sandwich shop.

http://www.wired.com/wiredscience/2013/05/twin-primes/2/

http://www.unh.edu/news/releases/2013/may/bp16zhang.cfm

http://www.nytimes.com/2013/05/21/science/solving-a-riddle-of-primes.html

For those not familiar with the conjecture, the twin primes conjecture is the following:

For every natural number k such that there are infinitely many prime pairs p and p' such that p'-p=2k

 

[jim mcnamara]

No, not the proof, just a big step forward. This problem was sort of relegated to the impossible pile. Zhang's approach got lots of other mathematicians to start thinking about it. For example Terry Tao has become interested and posted some results:

http://terrytao.wordpress.com/2013/06/23/the-distribution-of-primes-in-densely-divisible-moduli/

Now the problem is getting a lot of attention from people who pretty much ignored it in the past. This is good. Folks are cooperating in the polymath8 project:

http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes

 

[StatGuy2000]

I see. So it appears that Zhang's paper was advancing the research forward in thinking about the twin primes conjecture.

Admittedly, it's been over a decade since I last studied number theory, so much of Terry Tao's discussion is a little vague to me. This will be one of my pet projects -- to refresh myself with advanced math material!

 

[Yorshick]

I propose the following criteria of twin primes conjecture:
Natural numbers N1=6n+5 and N2=6n+7, n=0,1,2,3,..
are twins if and only if no one of three equations
n=6xy-x+y-1; x>=1; y>=1
n=6xy-x-y-1; x>=1; y>=x;
n=6xy+x+y-1; x>=1; y>=x;
has integer solution.
Attached: convenient C++ program for finding primes