M35
M35 | |
---|---|
Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 35 |
n-value : | 1,398,269 |
Number : | 814717564412...868451315711 |
Digits : | 420,921 |
Perfect number : | 2^{1,398,268} • (2^{1,398,269}-1) |
Digits : | 841,842 |
Discovery data : | |
Date of Discovery : | 1996-11-13 |
Discoverer : | Joel Armengaud |
Found with : | Lucas-Lehmer test / Prime95 on 90 MHz Pentium PC |
Credits : | George Woltman et. al. GIMPS |
M35 is the 35th Mersenne prime, both in order of size and date of discovery.
Specifically 2^{1,398,269}-1, written out in full 420,921 digits.
Discovered on 1996-11-13, this was the first prime discovered by GIMPS and the first Mersenne prime found by a personal computer. A little more than a month earlier, David Slowinski had found the previous Mersenne Prime on a Cray. This was to be the last discovered on a supercomputer or a mainframe.
Joel Armengaud, then a programmer from France, ran Prime95 on his Pentium 90Hz computer. The Lucas-Lehmer test took 88 hours to run. The primality of the number was confirmed by Slowinski. This showed the effectiveness of distributed computing.
This the time when the Pentium Bug was an issue. The fact that Prime95 was critical in uncovering this bug and then shortly there after found a prime, proved the program useful in both in testing PC's and that it could indeed find new primes.