# Found: new world record Twin Primes!

Author: Iain Bethune
Posted: 29 Sep 2016 | 13:55

Number Theory - the study of the integers - is perhaps one of the purest branches of maths and is not well-known for setting the headlines alight.

Along with the proof of Fermat's Last Theorem in 1995, which earned a knighthood for Sir Andrew Wiles, there was a lot of excitement about the Twin Prime Conjecture a few years ago, beginning a new spurt of progress towards the solution of this thorny mathematical problem.

The Twin Prime Conjecture says is that there are an infinite number of primes which occur in pairs with a difference of 2. For example, 3 and 5 are the first such pair, following by 5 and 7, 11 and 13, and so on. Since there are infinitely many primes it stands to reason that there should be infinitely many twin pairs... or does it? While it is widely believed that this is the case, infinities are a tricky business and the conjecture is (still) unproven, although at least we know there are infinitely many pairs separated by less than 246!

Why am I blogging about this today? Readers might recall previous posts about my involvement in the PrimeGrid project - one of the world's largest volunteer computing projects, it is dedicated to searching for large prime numbers. Just two weeks ago I woke up to the exciting news that one of the computers connected to PrimeGrid had discovered a new world record pair of Twin Primes: 2996863034895*21290000±1. This pair of primes has 388,342 digits each, nearly double the size of the previous record of 200700 digits, also found by PrimeGrid back in December 2011.

If you want to check you can download PDF copies (the '+1' prime and the '-1' prime) - 68 pages of Courier size 10 font for each - the first few hundred digits are in the image below. The lucky finder in this case was Tom Greer from the USA and you can read all about the details of the find in PrimeGrid's official announcement.

The actual computation used to prove primality of this pair of primes is quite short, taking only 23 minutes on an Intel Haswell CPU, but this downplays the size of the achievement. Since we started searching this range of numbers in Jul 2012, over 123.8 million candidates have been tested and 2531 primes were found (the rest of which turned out not to be twins), or roughly 5000 years of work on a single CPU core!

I'm planning some future blog posts explaining how PrimeGrid works, including some of the algorithms, software and volunteer computing infrastructure that we use. But for now, if you want to learn more why not join the project - it takes only 5 minutes to download and install the client software - and then you stand a chance of becoming the next world record holder!

### Author

Iain Bethune, EPCC