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Difference between revisions of "M32"
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| − | The '''32nd [[Mersenne prime]]''', both in size (smallest | + | {{InfoboxMersennePrime |
| + | | title=M32 | ||
| + | | rank=32 | ||
| + | | nvalue=756839 | ||
| + | | top5000id=25 | ||
| + | | digits=227832 | ||
| + | | number=174135906820...328544677887 | ||
| + | | pdigits=455663 | ||
| + | | discovery=1992-02-19 | ||
| + | | discoverer=[[David Slowinski]];[[Paul Gage]] | ||
| + | | foundwith=[[Lucas-Lehmer test]] / Maple on Harwell Lab [[Cray-2]] | ||
| + | }} | ||
| + | The '''32nd [[Mersenne prime]]''', both in size (smallest to largest) and in order of discover. | ||
(The last discovery before this was [[M29]], discovered out of order size-wise.) | (The last discovery before this was [[M29]], discovered out of order size-wise.) | ||
| − | :2<sup>756 | + | :2<sup>756 839</sup>-1, a number {{Num|227832}} [[decimal]] [[digit]] long was found to be [[prime]] on 1992-02-19. |
| − | This number was checked on a [[Cray Research|Cray]]-2 [[Classes of computers#Supercomputer|supercomputer]] at [https://en.wikipedia.org/wiki/Harwell_Science_and_Innovation_Campus Harwell] Lab in England, running the [[mprime (Cray)|mprime]] [[ | + | This number was checked on a [[Cray Research|Cray]]-2 [[Classes of computers#Supercomputer|supercomputer]] at [https://en.wikipedia.org/wiki/Harwell_Science_and_Innovation_Campus Harwell] Lab in England, running the [[mprime (Cray)|mprime]] [[software]] written by [[David Slowinski]] and [[Paul Gage]]. The calculation had finished some time prior to 19:00 1992-02-17. A technian (Adrian Powell?), had noticed the odd entry in the [[program]]s logfile at that time, but neither relised what it was nor could follow up. On the 19th, he could follow up and it was then that he 'discovered' the new prime. |
| − | The [[Lucas-Lehmer test]] had taken the machine 19 hours of [[CPU]] time to complete. Slowinski was notified and tested the number on a 16 CPU Cray-C90, taking about 3 hours. Later it was verified on a different computer architecture, using different software by [[Richard Crandall]], Chief Scientist at NeXT computer, at the time, in March of 1992. | + | The [[Lucas-Lehmer test]] had taken the machine 19 hours of [[CPU]] time to complete. Slowinski was notified and tested the number on a 16 CPU Cray-C90, taking about 3 hours. Later it was verified on a different computer architecture, using different software by [[Richard E. Crandall]], Chief Scientist at NeXT computer, at the time, in March of 1992. |
In Slowinski's book that is a print out of the number in full there is a note: | In Slowinski's book that is a print out of the number in full there is a note: | ||
| Line 14: | Line 26: | ||
==Sources== | ==Sources== | ||
*[http://primes.utm.edu/notes/756839.html The finding of the 32nd Mersenne] | *[http://primes.utm.edu/notes/756839.html The finding of the 32nd Mersenne] | ||
| − | [[Category:Mersenne | + | [[Category:Mersenne prime]] |
Latest revision as of 07:10, 17 October 2024
| M32 | |
|---|---|
| Prime class : | |
| Type : | Mersenne prime |
| Formula : | Mn = 2n - 1 |
| Prime data : | |
| Rank : | 32 |
| n-value : | 756,839 |
| Number : | 174135906820...328544677887 |
| Digits : | 227,832 |
| Perfect number : | 2756,838 • (2756,839-1) |
| Digits : | 455,663 |
| Discovery data : | |
| Date of Discovery : | 1992-02-19 |
| Discoverer : | David Slowinski Paul Gage |
| Found with : | Lucas-Lehmer test / Maple on Harwell Lab Cray-2 |
The 32nd Mersenne prime, both in size (smallest to largest) and in order of discover.
(The last discovery before this was M29, discovered out of order size-wise.)
This number was checked on a Cray-2 supercomputer at Harwell Lab in England, running the mprime software written by David Slowinski and Paul Gage. The calculation had finished some time prior to 19:00 1992-02-17. A technian (Adrian Powell?), had noticed the odd entry in the programs logfile at that time, but neither relised what it was nor could follow up. On the 19th, he could follow up and it was then that he 'discovered' the new prime.
The Lucas-Lehmer test had taken the machine 19 hours of CPU time to complete. Slowinski was notified and tested the number on a 16 CPU Cray-C90, taking about 3 hours. Later it was verified on a different computer architecture, using different software by Richard E. Crandall, Chief Scientist at NeXT computer, at the time, in March of 1992.
In Slowinski's book that is a print out of the number in full there is a note:
- "Took 26.562767 minutes to calculate using Maple 4.0 on a 512-MW 4 CPU Cray 2"
That may refer to the calculation of the decimal form of the number.
