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→How many prime numbers: + footnote: interesting ease of particular knowledge about this enormous number.
<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>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>
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>Multiple references:
* http://primes.utm.edu/largest.html
* The number two raised to successively larger powers cause the last three digits to fairly quickly begin repeating themselves in cycles of one hundred, so it is known that the last digits of this Mersenne prime end with ...951.</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 2015, only 48 Mersenne Primes have been found.<ref>http://primes.utm.edu/largest.html#largest</ref> The largest known prime, ''2<sup>57885161</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 2015, only 48 Mersenne Primes have been found.<ref>http://primes.utm.edu/largest.html#largest</ref> The largest known prime, ''2<sup>57885161</sup>-1'', is a Mersenne Prime. The concept of a Mersenne Prime was discovered by the French theologian, philosopher and mathematician [[Marin Mersenne]].