Yitang Zhang and The Twin Primes Conjecture

In early May 2013 a lecture was announced at Harvard university, which got a lot of mathematicians (especially the analytic number theorists) cautiously excited. A person by the name of Yitang Zhang had announced a proof of a theorem which could be considered a first step towards the Twin Primes conjecture — long standing in the theory of numbers. The conjecture is easy to state; so easy, in fact, that it would not be surprising for anyone who spends a few moments thinking about to come up with it.
To state the conjecture we recall some facts about prime numbers. A prime number is a number not divisible by any number other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, . . . . With a few moments thought one might wonder: Are there only infinitely many such numbers, or does the list go on forever? Over two thousand years ago, the Greek mathematician Euclid showed that there are infinitely many prime numbers.
 
(Editor’s note: The companion article in this issue by V G Tikekar gives several proofs of this assertion. We even have a proof in verse, by guest columnist Ben Orlin.)
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