M45
M45 | |
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Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 45 |
n-value : | 37,156,667 |
Number : | 202254406890...022308220927 |
Digits : | 11,185,272 |
Perfect number : | 2^{37,156,666} • (2^{37,156,667}-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 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
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.