A mathematician virtually unknown to the experts in his field — a 50-something lecturer at the University of New Hampshire named Yitang Zhang gave a surprising shock the mathematical community a few months back. He showed that there exists infinitely many primes with difference equal to a a number around 70 million.
Recall that, twin prime conjecture says that there exist infinitely many prime pairs of the form (p1,p2) where the difference between them is exactly 2. For example 11, 12; 17, 19 etc.
The result proved by Zhang assumes importance since there has not been any result so far suggesting that there can be a fixed constant maximum distance between two primes one can attain.
Read the interesting article about the achievement at https://www.simonsfoundation.org/quanta/20130519-unheralded-mathematician-bridges-the-prime-gap/
There has been a lot of activity after the announcement of the result, and the gap has come down from 70 million to something else!
Read the rest of the story at https://www.simonsfoundation.org/quanta/20131119-together-and-alone-closing-the-prime-gap/