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# Difference between revisions of "M45"

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− | '''M45''' normally refers to 2<sup>37 | + | '''M45''' normally refers to 2<sup>37 156 667</sup>-1, the 45th [[Mersenne prime]] in order of size from the smallest to greatest. This is the primary usage and what is referred to in the rest of this article. For clarification about other possible usages refer to the [[Nomenclature and notation]] article. |

==Discovery== | ==Discovery== | ||

− | The number, <math>2^{37,156,667}-1</math>, was found on 2008-09-06, by a computer owned by [[Hans-Michael Elvenich]] of Germany. The computer was running [[Prime95]] on 2.83 GHz Intel Core 2 Duo [[CPU]]. | + | The number, <math>2^{37\,156\,667}-1</math>, was found on 2008-09-06, by a computer owned by [[Hans-Michael Elvenich]] of Germany. The computer was running [[Prime95]] on 2.83 GHz Intel Core 2 Duo [[CPU]]. |

In an interview Hans-Michael Elvenich, a German electrical engineer and prime number enthusiast, stated: "After four years of searching for a prime on [[GIMPS]], finally a great success!" | In an interview Hans-Michael Elvenich, a German electrical engineer and prime number enthusiast, stated: "After four years of searching for a prime on [[GIMPS]], finally a great success!" | ||

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M45 was actually the 46th Mersenne prime found. M45, [[M46]], and [[M47]] were discovered in the following order of M47, M45 (2 weeks later), then M46 (8 months later). | M45 was actually the 46th Mersenne prime found. M45, [[M46]], and [[M47]] were discovered in the following order of M47, M45 (2 weeks later), then M46 (8 months later). | ||

− | It is 11 | + | It is 11 185 272 [[decimal]] [[digit]]s long. This was the second [[prime]] number known to be more that [[ten million digits]] long. Had it been found just before M47, ''it'' would have been responsible for [[GIMPS]] winning the [[EFF prizes|EFF prize]]. |

==External links== | ==External links== | ||

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*[https://www.mersenne.org/primes/Known Mersenne primes] at [[GIMPS]] | *[https://www.mersenne.org/primes/Known Mersenne primes] at [[GIMPS]] | ||

*[http://www.mersenneforum.org/txt/45.txt Number as text file (11 MByte)] | *[http://www.mersenneforum.org/txt/45.txt Number as text file (11 MByte)] | ||

− | [[Category:Mersenne | + | [[Category:Mersenne prime]] |

## Revision as of 22:35, 5 February 2019

**M45** normally refers to 2^{37 156 667}-1, the 45th Mersenne prime in order of size from the smallest to greatest. This is the primary usage and what is referred to in the rest of this article. For clarification about other possible usages refer to the Nomenclature and notation article.

## Discovery

The number, [math]\displaystyle{ 2^{37\,156\,667}-1 }[/math], was found on 2008-09-06, by a computer owned by Hans-Michael Elvenich of Germany. The computer was running Prime95 on 2.83 GHz Intel Core 2 Duo CPU.

In an interview Hans-Michael Elvenich, a German electrical engineer and prime number enthusiast, stated: "After four years of searching for a prime on GIMPS, finally a great success!"

M45 was actually the 46th Mersenne prime found. M45, M46, and M47 were discovered in the following order of M47, M45 (2 weeks later), then M46 (8 months later).

It is 11 185 272 decimal digits long. This was the second prime number known to be more that ten million digits long. Had it been found just before M47, *it* would have been responsible for GIMPS winning the EFF prize.