# Math Help - Factorial proofs

1. ## Factorial proofs

Prove that the following numbers are composite: 1000!+2 and 1000!+3

2. Originally Posted by algebrapro18
Prove that the following numbers are composite: 1000!+2 and 1000!+3
2 divides 1000! + 2

and 3 divides 1000! + 3

do you recall what 1000! means?

3. Originally Posted by algebrapro18
Prove that the following numbers are composite: 1000!+2 and 1000!+3
1000! + 2 is even. Therefore ........

1000! + 3 = 3 [(1)(2)(4)(5) ....... (1000) + 1] and so clearly has positive divisor other than one or itself ......

4. Using this idea we can prove that we consecutive composite numbers has no bound to it. Because $n!+2,n!+3,...,n!+n$ are all composite thus we can make the list of composites as long as we wish.

5. This is the basis for a classic Challenger:

Find 99 consecutive composite numbers.