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

## 919444^{1048576} + 1 is six MEELLION digits long and the twelfth biggest prime ever found

Humanity's collection of the very large prime numbers just grew by one member: 919444^{1048576} + 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, 2^{74207281} -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, 2^{74,207,281} − 1. The largest non-Mersenne prime, 10223*2^{31172165} + 1.

Mersenne primes are those that take the form of M_{n} = 2^{n} − 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. ®