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Primary Problem (Posted on 2002-08-21) Difficulty: 4 of 5
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,

n being the amount of primes.

Now we shall assume that the integer obtained by multiplying the primes is "N".

Therefore N = (p1 p2

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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionInfinite primesMath Man2011-02-04 22:08:10
SolutionPuzzle SolutionK Sengupta2007-03-30 10:33:31
re: your problem is technically wrongnikki2004-10-19 12:27:58
your problem is technically wrongBon2004-10-19 04:25:53
Here's a stabLawrence2003-08-27 18:49:42
Something curious...Fernando2003-03-25 14:42:16
re(2): suppose notTomM2002-12-13 08:18:25
re(2): suppose notCory Taylor2002-12-13 08:13:26
re: suppose notpeter pan2002-12-13 06:02:46
I love..cges2002-12-06 04:37:00
re: suppose notRebecca2002-12-05 12:39:54
Solutionsuppose notdanny2002-11-04 14:57:59
SolutionSolutionfriedlinguini2002-08-21 05:40:18
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