MATHEMATICS LOVERS PLEASE READ IT CAREFULLY........ Yesterday, two – yes two! – dramatic developments in the theory of prime numbers were announced. Both are – if correct – major theorems in their own right. Both can also be seen as steps towards the very biggest questions in the subject. (For those who came in late: remember that a prime is a whole number like 7, which can’t be divided by anything except itself and 1. So 6 is non-prime as it is divisible by 2.) Twin Primes It has long been observed that prime numbers sometimes come in pairs: 3 & 5, 17 & 19, 29 & 31, 821 & 823,… The Twin Prime Conjecture asserts, very simply, that this list goes on forever: there are infinitely many pairs of twin primes, meaning pairs (a) and (b) where (b=a+2). This is an old open problem which has left numerous clever people scratching their heads down the centuries. Although the list of known twin primes has grown ever longer (as of 2013, the record holders are 200700 digits long!), no-one has managed to prove it for certain. Yesterday at Harvard Yitang Zhang announced a proof, not of the full twin prime conjecture, but of a weaker result: that there are infinitely many pairs of primes (a) and (b) where (a < b leq a+70,000,000). Although this bound of 70 million is admittedly slightly bigger than 2, this is still a huge breakthrough, as it is the first time any result of this type has been proven. It establishes for the first time a very deep fact indeed: that even when you look at truly gigantic primes, you are guaranteed still to find some which are close together in an absolute and unwavering sense.
Posted on: Tue, 25 Jun 2013 03:26:25 +0000
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