New Mersenne prime found

Mersenne numbers have the form 2^p - 1. A Mersenne prime is a Mersenne number that is also a prime.

A new Mersenne prime discovery was announced today: 2^p - 1 is prime for p = 136279841. The size of the new Mersenne prime is consistent with what was predicted.

For many years now, the largest known prime has been a Mersenne prime. That is because there is an special algorithm for testing whether a Mersenne number is prime, the Lucas-Lehmer test. Because of this algorithm, Mersenne numbers can be tested for primality far more efficiently than can arbitrary numbers of comparable size.

There are now 52 known Mersenne primes, but the number just announced may not be the 52nd Mersenne prime. It has been confirmed that the 2^136279841 - 1 is prime, but it has not been confirmed that there are no Mersenne primes between the 51st Mersenne prime and the number just announced. There could be gaps.

If you were to write the latest Mersenne prime in hexadecimal, it would be a 1 followed by 34,069,960 F's.

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• Lucas numbers and Lucas pseudoprimes

The post New Mersenne prime found first appeared on John D. Cook.