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Wednesday, 27 January 2016

Largest Prime

The news of the discovery of a new, largest known prime broke about a week ago but I've only gotten around to writing about it here. It was of course a Mersenne prime discovered via GIMPS, the Great Internet Mersenne Prime Search. 

The number containing 22,338,618 digits is 274,207,2811 where 74,207,281 itself must be prime of course. It is the 49th known Mersenne prime defined as a prime expressible in the form 2p1 where p is prime. The first Mersenne primes are 3, 7, 31, and 127 corresponding to p values of 2, 3, 5, and 7 respectively. 

Note that p being prime is not sufficient to ensure that 2^p - 1 will be prime. As a counter example take p=11. The resulting number 2111=2047=23×89 is not prime. Here are links to some more interesting information about Mersenne primes:
on 27th of October 2024

Update: 2136,279,8411 has 41,024,320 digits and is prime! Read all about the new largest prime number ever found: Stand-up MathsYouTube video.

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