use gamma function to compute large factorials?

Euler's gamma function can be used to find the factorials of fractions and negative numbers by using integrals. For large factorials, this could be more efficient than multiplication.

How Euler Connected Pi (π), Square Root (√) and 1/2 with Factorials?

The online big number calculator only finds factorials of numbers less than 100,000.

Big Number Calculator

Willans' Formula for generating primes requires factorials. Thus, it is impractical for finding large primes using multiplication to compute factorials.

Willans' Formula -- from Wolfram MathWorld

Derpetology: Wilson's Theorem and A New Definition for Prime Numbers

***

Wilson's Theorem states that if p is prime, then the expression 1 + (p - 1)! is divisible by p. 

For example, if p = 5, we get 

1 + (5 - 1)! = 1 + 4!

1 +24 = 25

25/5 = 5

Another way of saying this is that 25 divided by 5 with a modulus of 5 is 0, because there is no remainder.

Unfortunately, factorials rapidly increase in magnitude. The largest factorial the online calculator Desmos can compute is 169 which has 300 or so digits. 

***