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

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- Dec 1st 2009, 05:28 PMkoko2009factorizations
how to Find factorizations of 974!+2 by using algorithms

- Dec 1st 2009, 09:07 PMBacterius
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. - Dec 2nd 2009, 02:53 AMaidan
It should be obvious that 2 is a factor.

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

Test $\displaystyle \left( \dfrac{974!}{2} + 1\right)$ 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. - Dec 2nd 2009, 02:56 AMBacterius
Try a Miller-Rabin test, maybe ? Or an AKS test to rub off doubts ...