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Line 65: − ===The Largest Known Prime=== − − The largest known prime is ''2<sup>32582657</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> − − ===Mersenne Prime=== − 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 April, 2007, only 44 Mersenne Primes have been found. The largest known prime ''2<sup>32582657</sup>-1'', is a Mersenne Prime. The concept of a Mersenne Prime was discovered by the French theologian, philosopher and mathematician [[Marin Mersenne]].
the largest known prime, and mersnne primes, are not really open questions
Another proof that there are infinitely many primes shows something stronger, namely the sum of the reciprocals of primes less than n "grows like" log(log(n)):
Another proof that there are infinitely many primes shows something stronger, namely the sum of the reciprocals of primes less than n "grows like" log(log(n)):
<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>32582657</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>
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 April, 2007, only 44 Mersenne Primes have been found. The largest known prime ''2<sup>32582657</sup>-1'', is a Mersenne Prime. The concept of a Mersenne Prime was discovered by the French theologian, philosopher and mathematician [[Marin Mersenne]].
==Unique Factorization==
==Unique Factorization==
==Open Problems about Prime Numbers==
==Open Problems about Prime Numbers==
===Twin primes===
===Twin primes===