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→How many prime numbers: updated largest prime number as of today.
<math>\sum_{p\le x}p^{-1}\approx\log\log x</math>
<math>\sum_{p\le x}p^{-1}\approx\log\log x</math>
The largest known prime is ''2<sup>43112609</sup>-1''; it was discovered by the '''Great Internet Mersenne Prime Search''' ('''GIMPS''')<ref>http://www.mersenne.org/</ref>, a distributed computing project launched by George Woltman in early 1996.<ref>http://primes.utm.edu/largest.html</ref>
The largest known prime is ''2<sup>57885161</sup>-1''; it was discovered in 2013 by Curtis Cooper with the '''Great Internet Mersenne Prime Search''' ('''GIMPS''')<ref>http://www.mersenne.org/</ref>, a distributed computing project launched by George Woltman in early 1996.<ref>http://primes.utm.edu/largest.html</ref>
A '''Mersenne prime''' is a prime number ''M'' that is of the form ''M = 2<sup>n</sup> − 1'', where ''n'' is some [[prime number]]<ref>[http://mathworld.wolfram.com/MersennePrime.html Mersenne Prime] from Wolfram</ref>. As of 2012, only 47 Mersenne Primes have been found.<ref>http://primes.utm.edu/largest.html#largest</ref> The largest known prime, ''2<sup>43112609</sup>-1'', is a Mersenne Prime. The concept of a Mersenne Prime was discovered by the French theologian, philosopher and mathematician [[Marin Mersenne]].
A '''Mersenne prime''' is a prime number ''M'' that is of the form ''M = 2<sup>n</sup> − 1'', where ''n'' is some [[prime number]]<ref>[http://mathworld.wolfram.com/MersennePrime.html Mersenne Prime] from Wolfram</ref>. As of 2012, only 47 Mersenne Primes have been found.<ref>http://primes.utm.edu/largest.html#largest</ref> The largest known prime, ''2<sup>43112609</sup>-1'', is a Mersenne Prime. The concept of a Mersenne Prime was discovered by the French theologian, philosopher and mathematician [[Marin Mersenne]].