M32

From Prime-Wiki
Jump to: navigation, search
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.)

2756 839-1, a number 227,832 decimal digit long was found to be prime on 1992-02-19.

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 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.

Sources