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 $(p_1, p_2)$ 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/
