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Difference between revisions of "M51"
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{{InfoboxMersennePrime | {{InfoboxMersennePrime | ||
| − | | title= M51 | + | | title=M51 |
| − | | rank= 51 | + | | rank=51 |
| − | | nvalue= | + | | nvalue=82589933 |
| top5000id=125874 | | top5000id=125874 | ||
| − | | digits= | + | | digits=24862048 |
| − | | pdigits= | + | | pdigits=49724095 |
| + | | number=148894445742...325217902591 | ||
| discovery=2018-12-07 | | discovery=2018-12-07 | ||
| discoverer=[[Patrick Laroche]] | | discoverer=[[Patrick Laroche]] | ||
| − | | | + | | foundwith=[[Lucas-Lehmer test]];[[Prime95]] on Intel i5-4590T @ 2.0GHz |
| − | | | + | | credits=[[George Woltman]];[[Aaron Blosser]] et. al.;([[GIMPS]] & [[PrimeNet]]) |
| − | |||
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}} | }} | ||
| − | '''M51''' normally refers to the | + | '''M51''' normally refers to the 51st [[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. |
==Discovery== | ==Discovery== | ||
| − | The official discovery date for prime {{Greatest Mersenne Prime| | + | The official discovery date for prime {{Greatest Mersenne Prime|only}} was 2018-12-21 and has {{Num|24862048}} [[digit]]s. |
A computer volunteered by [[Patrick Laroche]] made the find on 2018-12-07. The primality proof took twelve days of non-stop computing on a machine with an Intel i5-4590T CPU. | A computer volunteered by [[Patrick Laroche]] made the find on 2018-12-07. The primality proof took twelve days of non-stop computing on a machine with an Intel i5-4590T CPU. | ||
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==Verification== | ==Verification== | ||
| − | To confirm that there were no errors in the [[ | + | To confirm that there were no errors in the [[hardware]] or [[software]], the number had to be independently verified by running tests on various machines with different architecture and software. |
The volunteers that ran these tests were: | The volunteers that ran these tests were: | ||
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==External links== | ==External links== | ||
*[https://www.mersenne.org/primes/?press=M82589933 Official press release by GIMPS] | *[https://www.mersenne.org/primes/?press=M82589933 Official press release by GIMPS] | ||
| + | *[https://www.mersenneforum.org/showthread.php?t=23877 Discovery thread] at [[MersenneForum]] | ||
| + | |||
[[Category:Mersenne prime]] | [[Category:Mersenne prime]] | ||
Latest revision as of 05:53, 21 July 2021
| M51 | |
|---|---|
| Prime class : | |
| Type : | Mersenne prime |
| Formula : | Mn = 2n - 1 |
| Prime data : | |
| Rank : | 51 (Provisional ranking) |
| n-value : | 82,589,933 |
| Number : | 148894445742...325217902591 |
| Digits : | 24,862,048 |
| Perfect number : | 282,589,932 • (282,589,933-1) |
| Digits : | 49,724,095 |
| Discovery data : | |
| Date of Discovery : | 2018-12-07 |
| Discoverer : | Patrick Laroche |
| Found with : | Lucas-Lehmer test Prime95 on Intel i5-4590T @ 2.0GHz |
| Credits : | George Woltman Aaron Blosser et. al. (GIMPS & PrimeNet) |
M51 normally refers to the 51st 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.
Discovery
The official discovery date for prime 2136,279,841-1 was 2018-12-21 and has 24,862,048 digits.
A computer volunteered by Patrick Laroche made the find on 2018-12-07. The primality proof took twelve days of non-stop computing on a machine with an Intel i5-4590T CPU.
The official credit for the discovery goes to "P. Laroche, G. Woltman, A. Blosser, et al.".
Verification
To confirm that there were no errors in the hardware or software, the number had to be independently verified by running tests on various machines with different architecture and software.
The volunteers that ran these tests were:
- Andreas Höglund verified the prime using CUDALucas running on a NVidia V100 GPU in 21 hours.
- Andreas Höglund also verified the prime using Mlucas running on 16 cores of an Amazon AWS instance in 72 hours.
- Aaron Blosser also verified it using Prime95 on an Intel 7700K processor in 6 days, 8 hours.
