# factorizations

• December 1st 2009, 05:28 PM
koko2009
factorizations
how to Find factorizations of 974!+2 by using algorithms
• December 1st 2009, 09:07 PM
Bacterius
I suspect this number has a lot of possible factorizations. You could use the elliptic curve factorization algorithm, it works remarkably smoothly for numbers with many possible factorizations.
Or maybe there's some arithmetic trick to simplify this, I do not know.
• December 2nd 2009, 02:53 AM
aidan
Quote:

Originally Posted by koko2009
how to Find factorizations of 974!+2 by using algorithms

It should be obvious that 2 is a factor.

$2 \left( \dfrac{974!}{2} + 1\right) = 974! + 2$

Test $\left( \dfrac{974!}{2} + 1\right)$ for primality.

Most likely it is a prime number.
I did a Fermat test for several hundred primes.
ALL results indicated that the number is prime.
• December 2nd 2009, 02:56 AM
Bacterius
Try a Miller-Rabin test, maybe ? Or an AKS test to rub off doubts ...