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Difference between revisions of "M45"

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'''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.
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{{InfoboxMersennePrime
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| title=M45
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| rank=45
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| nvalue=37156667
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| top5000id=85528
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| digits=11185272
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| number=202254406890...022308220927
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| pdigits=22370543
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| discovery=2008-09-06
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| discoverer=[[Hans-Michael Elvenich]]
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| foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2.83 GHz Core 2 Duo [[Personal computer|PC]]
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| credits=[[George Woltman]] et. al.;[[GIMPS]]
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}}
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'''M45''' normally refers to 2<sup>{{Num|37156667}}</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]].
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M45 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 11,185,272 [[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]].
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It is {{Num|11185272}} [[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 primes]]
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[[Category:Mersenne prime]]

Latest revision as of 11:40, 18 February 2019

M45
Prime class :
Type : Mersenne prime
Formula : Mn = 2n - 1
Prime data :
Rank : 45
n-value : 37,156,667
Number : 202254406890...022308220927
Digits : 11,185,272
Perfect number : 237,156,666 • (237,156,667-1)
Digits : 22,370,543
Discovery data :
Date of Discovery : 2008-09-06
Discoverer : Hans-Michael Elvenich
Found with : Lucas-Lehmer test / Prime95 on 2.83 GHz Core 2 Duo PC
Credits : George Woltman et. al.
GIMPS

M45 normally refers to 237,156,667-1, 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

M45 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.

External links