M43
M43 | |
---|---|
Prime class : | |
Type : | Mersenne prime |
Formula : | M_{n} = 2^{n} - 1 |
Prime data : | |
Rank : | 43 |
n-value : | 30,402,457 |
Number : | 315416475618...411652943871 |
Digits : | 9,152,052 |
Perfect number : | 2^{30,402,456} • (2^{30,402,457}-1) |
Digits : | 18,304,103 |
Discovery data : | |
Date of Discovery : | 2005-12-15 |
Discoverer : | Curtis Cooper Steven Boone |
Found with : | Lucas-Lehmer test / Prime95 on 2 GHz Pentium 4 PC |
Credits : | George Woltman et. al. GIMPS |
M43 is the short hand used to refer to the 43rd Mersenne prime 2^{30,402,457}-1.
The number is 9,152,052 decimal digits long.
Discovery
M43 was discovered to be prime on 2005-12-15 by Curtis Cooper and Steven Boone, using Prime95 written by George Woltman. At time of its discovery, it was the largest known prime.
This prime number was the ninth record prime found by the GIMPS project.
Verification
The new prime was independently verified:
- by Tony Reix of Bull S.A. in Grenoble, France, in 5 days using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program;
- by Jeff Gilchrist of Elytra Enterprises Inc. in Ottawa, Canada, in 14 days using 14 CPUs of a Compaq Alpha GS160 1.2 GHz CPU server at SHARCNET.
External links
- GIMPS Discovers 43rd Mersenne Prime (press release)