Is there a fast way to determine if this is a prime number?

Yes, there is. And yes, it is prime.

http://www.math.com/students/calculators/source/pr...

I don't think there's a way to tell, but you can just eliminate the usual factors. Here's how:

The number doesn't end with an even number. So it's not a multiple of 2.

If you add up all the digits in the number, and it adds up to a multiple of 3, then the number is a multiple of three. 1+2+2+5+4+7+8+3=32 which is not a multiple of 3. So the number isn't a multiple of three.

Since it doesn't end with 5 or 0, it can't be a multiple of 5.

If it's not a multiple of 2 nor 3, it can't be a multiple of 6.

If it's not a multiple of 2 nor 4, it can't be a multiple of 8.

If it's not a multiple of 3, it can't be a multiple of 9.

So that leaves you with it being a multiple of 7, 13, 17,19, etc. You just have to manually divide to check those.

Hope that helps.

For large numbers that aren't divisible by anything obvious (2, 3, 5), you end up having to try dividing it by every prime from 2 up to the square root of the number. Even for 3-digit numbers, this can take a long time. For your 8-digit number, forget about it. The only fast way is to run it through a computer program, like the one linked above.