- #1
numbthenoob
- 10
- 0
Is there a name and/or proof for the following conjecture?
"For any prime p, p! is congruent to p2-p modulo p2."
Thanks much.
"For any prime p, p! is congruent to p2-p modulo p2."
Thanks much.
A factorial of a prime number is the product of that prime number and all the positive integers that are smaller than it. For example, the factorial of 5 (denoted as 5!) is equal to 5 x 4 x 3 x 2 x 1 = 120.
Factorials of prime numbers are important in various mathematical calculations, such as in combinatorics and probability. They are also used in the calculation of permutations and combinations.
The largest factorial of a prime number is 13! which is equal to 6,227,020,800.
No, factorials of prime numbers are not always prime numbers. For example, the factorial of 5 (5!) is 120, which is not a prime number.
No, factorials of prime numbers cannot be negative. They are always positive integers.