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New Mersenne primes not discovered

The Great Internet Mersenne Prime Search, the premier distributed-computing prime finding initiative, has reported that $M_{32582657} = 2^{32,582,657}-1$, the 44th Mersenne prime to be discovered, is also the 44th Mersenne Prime in numerical order. It was found by Steven Boone and Curtis Cooper in 2006 (Cooper also discovered the current largest prime as reported here in February), but until now it was not known for certain that other, smaller primes had not been overlooked. GIMPS has now checked all the intervening Mersenne numbers for primality and having found nothing, $M_{32582657}$ is secure in its 44th-ness.

Further information

The Great Internet Mersenne Prime Search (announcement on the front page as of November 10)

Their page for the prime itself

Mersenne Prime at Wolfram Mathworld

via @mathupdate on Twitter

More experimental evidence for the infinitude of the primes

In a classic example of the intersection between maths and news, there’s been a new Mersenne prime discovered! Mersenne primes are numbers of the form $2^p – 1$, where $p$ is a prime number. They’re highly valued as a source of large prime numbers, since testing the primality of a (suspected) prime of this form is much easier than for general prime numbers.

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