# Found the largest generalized number Farm

On August 29, 2017 at 14:15:23 UTC, the participants of the PrimeGrid voluntary distributed computing project found another large prime number:



${919444}^{1048576}+1$

This number with 6,253,210 characters has been entered into the Base of the largest known prime numbers by Professor Chris Caldwell as the largest known generalized Fermat number and the 12th known prime number in size.

Fermat generalized numbers are ${{a}^{2}}^{n}+{{b}^{2}}^{n}$${a ^ 2} ^ n + {b ^ 2} ^ n$and number ${919444}^{1048576}+1$$919444 ^ {1048576} + 1$fits this pattern.

This number was the first generalized number Farm for $n=20$$n = 20$and generally the second simple number that the participants of the distributed computing project PrimeGrid found.

Good luck fell on the computer of American Sylvanus Zimmerman (Sylvanus A. Zimmerman). He has a computer with an Nvidia GeForce GTX 1060 graphics card and an Intel Xeon E3-1225 v3 processor at 3.20 GHz with 8 GB of RAM running the Windows 10 Professional Edition operating system. The verification of a probable prime number (PRP) on its GPU took 4 hours and 43 minutes. Zimmerman himself is a member of the Aggie The Pew .

Rechecking this prime number using a specially written verification program took 3 days, 23 hours and 53 minutes of computing on an Intel Core i7-7700K computer at 4.20 GHz with 16 GB of RAM, also under Windows 10 Professional Edition.

Of course, on a single computer, the search for such a large simple number would take many years or decades, so the discovery would have been impossible without hundreds of other participants who donated their computing resources on idle processors.

The largest number known to mankind is still ${2}^{74207281}-1$$2 ^ {74207281} -1$c 22 338 618 characters. This is the number of Mersenne, that is, the number of the form ${2}^{n}-1$$2 ^ n-1$. The largest prime number that is not the Mersenne number is $10,223×{2}^{31172165}+1$$10,223 × 2 ^ {31172165} + 1$.

All Articles