I am not aware of any SIMPLE methods to do your job.
As far as I know you simply have to divide by primes up to the square root of the number (something in excess of 2800 for this number).
Of course you can eliminate simple ones easily: not even so not 2, sum of digits not divisible by 3 so not 3,
last digit not 0 or 5 so not 5, not divisible by 7 or 11...and as far as I know you just go from there.
The sieve of Eratosthenes may help but for a number like this one it doesn't help much; there are other sieves which you should check out online.
