# A New Factor of F13

F13 = 2213 = 28192 + 1 is the 13-th Fermat number.

At 19 June 1995 three prime factors of F13 were known:

F13 = 2710954639361 . 2663848877152141313 . 3603109844542291969 . c2417

The 13-digit factor was found by Hallyburton and Brillhart in 1974.
The 19-digit factors were found by Richard Crandall on Zilla net
(a network of NeXT workstations) in January and May 1991.

The quotient c2417 is a composite number with 2417 decimal digits.

On 19 June 1995 I found a fourth factor with 27 decimal digits:

The quotient is c2391, a composite number with 2391 decimal digits.

## The Computation

The computation to find p27 used Lenstra's elliptic curve method (ECM)
implemented on a 40 Mhz IBM 80386 PC with a Dubner Cruncher board to speed up the multiple-precision arithmetic. Overall, it took about 47 days to find the factor (my current program would take about 30 days).

## The Cruncher versus Supercomputers

On large numbers like F13, the Cruncher is about twice as fast as the Fujitsu VP100 which I used to factorise F11 back in 1988:

F11 = 319489 . 974849 . 167988556341760475137 . 3560841906445833920513 . p564,

where p564 is a 564-digit prime number.

Since the Cruncher costs only a few thousand dollars, it is a very cost-effective
"factoring engine".