# Factorial proofs

• Feb 24th 2008, 05:33 PM
algebrapro18
Factorial proofs
Prove that the following numbers are composite: 1000!+2 and 1000!+3
• Feb 24th 2008, 05:42 PM
Jhevon
Quote:

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?
• Feb 24th 2008, 05:44 PM
mr fantastic
Quote:

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 ......
• Feb 24th 2008, 07:32 PM
ThePerfectHacker
Using this idea we can prove that we consecutive composite numbers has no bound to it. Because \$\displaystyle n!+2,n!+3,...,n!+n\$ are all composite thus we can make the list of composites as long as we wish.
• Feb 24th 2008, 08:10 PM
Soroban
This is the basis for a classic Challenger:

Find 99 consecutive composite numbers.