M25

The 25th Mersenne prime, in order from smallest to largest and in order of discovery.

M25 is [math]\displaystyle{ 2^{21,701}{-}1 }[/math], a number of 6,533 digits.

Two high school students, Landon Curt Noll and Laura A. Nickel (later Ariel Glenn) who were studying number theory California State University, Hayward (while still in high school) with Dr. Derrick Henry Lehmer of UC Berkeley and Dr. Jurca of CSUH, programmed (in assembly language) the University's CDC Cyber 174 mainframe computer to perform the Lucas-Lehmer test for primality. They consulted work previously done by Gillies and Tuckerman. This showed that all candidate exponents up to M(21000) had been tested. They consulted Wagstaff's factor table to eliminate more candidates (31 of 75). There was a theory that there was an 'Island of Mersenne Primes'. They were testing this theory and that Tuckerman's discovery of M24 ([math]\displaystyle{ 2^{19,937}{-}1 }[/math]) was the start of this island.

On October 30, 1978, after a testing time (for this number alone) of 7 hours, 40 minutes and 20 seconds, [math]\displaystyle{ 2^{21,701}{-}1 }[/math] was shown to have residue of 0 (zero) at the end of the L-L test, meaning that it is prime. This result was verified by Tuckerman of IBM's Watson Research Center and by Lehmer at UC Berkeley.

After the discovery of the prime, they as a team tested no more candidates, although Noll continued alone (discovering M26) and reworked the program.

Sources

• Mathmatics of Computation, vol.35, num. 152 October 1980, pp 1387-1390
• Noll at the Prime Pages
• Noll's website