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Give a boffin a Xeon and a big GPU, get a new big prime number

9194441048576 + 1 is six MEELLION digits long and the twelfth biggest prime ever found

By Richard Chirgwin, 5 Sep 2017

Humanity's collection of the very large prime numbers just grew by one member: 9194441048576 + 1.

The newly-found number lands in twelfth place on the list of largest prime numbers and, set down in full, would be 6,253,210 digits long (number one on the large primes list, 274207281 -1, is 22,338,618 digits long).

The number was submitted to the list of largest known prime numbers maintained by the University of Tennessee, here, on 2 September 2017.

And it didn't need a supercomputer to find: one Sylvanus Zimmerman, part of the Aggie the Pew team, found the number with an Nvidia GeForce GTX 1060 in an Intel Xeon E3-1225 v3 CPU at 3.20GHz with 8GB RAM, running Microsoft Windows 10 Professional Edition. “This GPU took about 4 hours 43 minutes to probable prime (PRP) test with GeneferOCL4,” the PrimeGrid statement says.

The announcement adds “This is the first Generalized Fermat prime found for n=20, the second-largest prime found by PrimeGrid, and the second-largest non-Mersenne prime”.

Currently, the largest known prime number is a Mersenne prime, 274,207,281 − 1. The largest non-Mersenne prime, 10223*231172165 + 1.

Mersenne primes are those that take the form of Mn = 2n − 1; that form is named after 17th-century French priest, polymath and prime number investigator Marin Mersenne. Non-Mersenne primes take a variety of other forms.

Zimmerman's discovery was cross-checked on an Intel Core i7-7700K CPU @ 4.20GHz with 16GB RAM, running Microsoft Windows 10 Professional Edition. It took just seven minutes short of four days to check the prime number, using Jean Penné's LLR primality program. ®

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