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M46
M46 | |
---|---|
Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 46 |
n-value : | 42,643,801 |
Number : | 169873516452...765562314751 |
Digits : | 12,837,064 |
Perfect number : | 2^{42,643,800} • (2^{42,643,801}-1) |
Digits : | 25,674,127 |
Discovery data : | |
Date of Discovery : | 2009-04-12 |
Discoverer : | Odd Magnar Strindmo |
Found with : | Lucas-Lehmer test / Prime95 on 3 GHz Core 2 PC |
Credits : | George Woltman et. al. GIMPS |
M46 is the short hand used to refer to the 46th Mersenne prime 2^{42,643,801}-1.
The number is 12,837,064 decimal digits long. After the discovery, Dr. Crandalls company Perfectly Scientific, which developed the FFT algorithm used by GIMPS, made commemorative souvenir posters with all 12.8 million digits printed in a tiny font.
Discovery
M46 was discovered to be prime on 2009-04-12 by an IT professional Odd Magnar Strindmo, using Prime95 program written by George Woltman. Strindmo's computers had been working with GIMPS since 1996 testing over 1400 candidates. The calculation took 29 days on a 3.0 GHz Intel Core2 processor.
At time of its discovery, it was the second-largest known prime number. This prime number was the thirteenth record prime found by the GIMPS project.
Verification
The prime was first verified on June 12th by Tony Reix of Bull SAS in Grenoble, France, using the Glucas program running on Bull NovaScale HPC servers, one featuring Itanium2 CPUs and another featuring Nehalem CPUs.
The prime was later independently verified by Rob Giltrap of Sun Microsystems using Ernst Mayer's Mlucas program running on a Sun SPARC Enterprise M9000 Server.
External links
- GIMPS Discovers 47th Mersenne Prime (press release)