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 Primary Problem (Posted on 2002-08-21)
Prove that there exists an infinitely large number of primes.

 Submitted by Dulanjana Rating: 3.5000 (8 votes) Solution: (Hide) Suppose that there exists a finite amount of Primes and the list is as follows: (p1, p2, p3.....pn). n being the amount of primes. Now we shall assume that the integer obtained by multiplying the primes is "N". Therefore N = (p1 p2 p3.....pn). N is obviously not Prime because it is divisible by all the other primes. Now we shall add 1 to N. "N+1" will not be divisable by any of the other primes since it is not a multiple of the primes that were given. Hence N + 1 is a Prime. But N + 1 is also larger than any of the primes that were given, thus it contradicts our first assumption of the list given was complete. Therefore the list will have no end.

 Subject Author Date Infinite primes Math Man 2011-02-04 22:08:10 Puzzle Solution K Sengupta 2007-03-30 10:33:31 re: your problem is technically wrong nikki 2004-10-19 12:27:58 your problem is technically wrong Bon 2004-10-19 04:25:53 Here's a stab Lawrence 2003-08-27 18:49:42 Something curious... Fernando 2003-03-25 14:42:16 re(2): suppose not TomM 2002-12-13 08:18:25 re(2): suppose not Cory Taylor 2002-12-13 08:13:26 re: suppose not peter pan 2002-12-13 06:02:46 I love.. cges 2002-12-06 04:37:00 re: suppose not Rebecca 2002-12-05 12:39:54 suppose not danny 2002-11-04 14:57:59 Solution friedlinguini 2002-08-21 05:40:18

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