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