Hi noobard;

Theoretically yes but only for small numbers.

Supposing you wanted to test whether the repunit 1111111111111111111 were prime. You would have to compute 1111111111111111110! + 1 a number with 19568292231841581432 digits and mod it by 1111111111111111111.

Last edited by bobbym (2009-06-08 20:32:17)

I think bobbym's point is that, even for computers, the calculation of large factorials is not a very good way of testing if numbers are prime.

At university, if I type Factorization(1111111111111111111); into Magma I can't even tell that there is a delay before it prints [ <1111111111111111111, 1> ] confirming that 1111111111111111111 is indeed a prime.

If I type Factorial(1111111111111111111); instead it refuses to do the calculation because 1111111111111111111 is too large.

For Avon
Quote:

I think bobbym's point is that, even for computers, the calculation of large factorials is not a very good way of testing if numbers are prime.

At university, if I type Factorization(1111111111111111111); into Magma I can't even tell that there is a delay before it prints [ <1111111111111111111, 1> ] confirming that 1111111111111111111 is indeed a prime.

If I type Factorial(1111111111111111111); instead it refuses to do the calculation because 1111111111111111111 is too large.

RickIsAnIdiot

Can you type Factorization(1111111111111111111); into Magma ? And it shows all the digit,s ?

Hi Avon;

Magma is telling you that it is prime because it has the factors of itself and 1.

Me too.

Hi ganesh;

Yes, 721/7 = 103. Wilson's theorem works. That's a proof that 7 is prime. For larger primes the computation of the factorial mod n makes the idea unfeasible.