Factorials!

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how about a new random number game. Factorials!
these will go up VERY quickly, and I want the numbers in full!
also I think it would be interesting to put in the prime factorization as well.
(0!=1)
1! = 1 (there isn't a prime factorization for 1, unless you count 2^0)

What are we supposed to do?
y! = (x+1)!; where x = previous post and y = current post?

So . . .

2! = 2
prime factorization = umm . . . 2 * 2^0 . . .?

Is this how the game goes, or did I assume the rules incorrectly?

yes it is in the form (x+1)! where x is the previous post.
the reason I did 2^0 for 1 is because it isn't a prime number, and it isn't a multiple of any prime numbers. you could say 1 = x^1, where x is any number.
for the prime factorization, just do it in the form f = 2^a * 3^b * 5^c etc,

so 3! = (2+1)! = 6 = 2^1 * 3^1

4! = 24 = 2^3 * 3^1

5! = 120 = 2^3 * 3^1 * 5^1

6! = 720 = 2^4 * 3^2 * 5^1

It's going to start getting *really* exciting soon! I love BIG numbers!

7!=5040 = 2 ^ 4 x 3 ^ 2 x 5 x 7

Number of divisors: 60

8! = 40320 = 2^7 * 3^2 * 5 * 7

9! = 362,880 =2^7 * 3^4 * 5 * 7

yeah, I like big numbers too.

And pi, I like pi

10! = 3,628,800 = 2^8 * 3^4 * 5^2 * 7

pi is great but I like e better and phi the most. And, of course, the fibonacci sequence since it has connections with phi and it's fun to make it bigger and bigger. I often use fibonacci numbers in my art in various ways.

11!=39 916800 = 2 ^ 8 x 3 ^ 4 x 5 ^ 2 x 7 x 11

12! = 479,001,600 = 2^10 * 3^5 * 5^2 * 7 * 11

Yay, Richie: you added a new prime!

13!=6227 020800 = 2 ^ 10 x 3 ^ 5 x 5 ^ 2 x 7 x 11 x 13

14! = 87,178,291,200 = 2^11 * 3^5 * 5^2 * 7^2 * 11 * 13

15!=1 307674 368000 = 2 ^ 11 x 3 ^ 6 x 5 ^ 3 x 7 ^ 2 x 11 x 13

16! = 20,922,789,888,000 = 2^15 * 3^6 * 5^3 * 7^2 * 11 * 13