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

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- Feb 24th 2008, 05:33 PMalgebrapro18Factorial proofs
Prove that the following numbers are composite: 1000!+2 and 1000!+3

- Feb 24th 2008, 05:42 PMJhevon
- Feb 24th 2008, 05:44 PMmr fantastic
- Feb 24th 2008, 07:32 PMThePerfectHacker
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 PMSoroban
This is the basis for a classic Challenger:

Find 99 consecutive composite numbers.

Answer (drag your cursor between the asterisks)

* 100! + n, for n = 2,3,4,5, ... , 100 *