From the not-sure-why-but-it's-interesting department:
https://www.simonsfoundation.org/features/science-news/unheralded-mathematician-bridges-the-prime-gap/
...
Primes are often much closer together than the average predicts, or much
farther apart. In particular, “twin” primes often crop up — pairs such
as 3 and 5, or 11 and 13, that differ by only 2. And while such pairs
get rarer among larger numbers, twin primes never seem to disappear
completely (the largest pair discovered so far is 3,756,801,695,685 x
2666,669 – 1 and 3,756,801,695,685 x 2666,669 + 1).
For hundreds of years, mathematicians have speculated that there are
infinitely many twin prime pairs. In 1849, French mathematician Alphonse
de Polignac extended this conjecture to the idea that there should be
infinitely many prime pairs for any possible finite gap, not just 2.
Since that time, the intrinsic appeal of these conjectures has given
them the status of a mathematical holy grail, even though they have no
known applications. But despite many efforts at proving them,
mathematicians weren’t able to rule out the possibility that the gaps
between primes grow and grow, eventually exceeding any particular bound.
Now Zhang has broken through this barrier. His paper shows that there is
some number N smaller than 70 million such that there are infinitely
many pairs of primes that differ by N. No matter how far you go into the
deserts of the truly gargantuan prime numbers — no matter how sparse the
primes become — you will keep finding prime pairs that differ by less
than 70 million.
...
_______________________________________________
cryptography mailing list
[email protected]
http://lists.randombit.net/mailman/listinfo/cryptography
