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Math Help - Factorial proofs

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    Factorial proofs

    Prove that the following numbers are composite: 1000!+2 and 1000!+3
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    Quote Originally Posted by algebrapro18 View Post
    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?
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    Quote Originally Posted by algebrapro18 View Post
    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 ......
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    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.
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    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 *

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