## M74207281 is prime!

I’m a bit late to the party, but the Great Internet Mersenne Prime Search has recently announced a newly verified prime number, $M_{74207281} = 2^{74207281} - 1$, with a whopping 22,338,618 decimal digits! This is now the largest known prime number (though of course there are infinitely many larger ones). For some perspective, the King James Version of the bible has only just over 3 million letters, one-seventh as many as the number of digits in the new prime. For more perspective on how big this number is, check out this Numberphile video, in which Matt Parker actually gets the whole thing printed out… in 3 volumes… with a really tiny font!

Apparently a computer found the prime on my son’s fourth birthday, September 17, 2015, but the automatic notification system failed and no human noticed it until almost 4 months later, on January 7! This raises some interesting “if a tree falls in a forest”-type questions, but in any case, the tradition is that the official date of discovery of a new prime is when a human first sees it.

I’ve previously reported on a few other announcements of newly discovered Mersenne primes by GIMPS: here, here, here, and here, though it seems I also missed a couple. I also wrote a 30-part series in November, beginning here, on the math behind the Lucas-Lehmer test which is used to find prime Mersenne numbers.