Gaps between Twin Primes

Today I turned 24917 days old. This number is prime and forms a twin prime with 24919. One claim that 24917 has to fame is that it marks the end of a gap of 496 between consecutive twin primes. After 24421 (the larger of twin pairs), there is a gap of 496 numbers until 24917 (the smaller of twin primes).

Source

At the right is a list of the record breaks. Of course, I won't live to experience the next record gap of 628 days between 62299 and 62927. However, I won't have to wait long until the next twin prime pair: 24917 and 24919. There is a gap of only 58 days between 24919 and 24977.

Of course, there's a lot of interest as to whether twin primes go on forever. It's very likely of course but it hasn't been proven. Progress has been made recently however, by Yitang Zhang, James Maynard and Terence Tao with his Polymath Project. The breakthrough relates specifically to the gaps between prime numbers rather than the gaps between successive pairs of twin prime numbers. There's a good account of these developments in this article from quantamagazine.

In any case, I felt it was important to celebrate the end of this latest record gap as my endless, numbered days unravel.