Anybody need an eye opener?
Atheists are always demanding proof of things, so I've decided to give them proof:
Suppose (for the sake of contradiction) we have a complete list of primes.
Call the primes in our finite list p1, p2, ..., pr.
Let P be any common multiple of these primes plus one (for example, P = p1p2...pr+1). Now P is either prime or it is not. If it is prime, then P is a prime that was not in our list.
If P is not prime, then it is divisible by some prime, call it p. Notice p can not be any of p1, p2, ..., pr, otherwise p would divide 1, which is impossible.
So this prime p is some prime that was not in our original list. Either way, the original list was incomplete.
Therefore there are infinitely many primes.
You can't tell me that's not a valid proof.
Take that, Euclidlutionists.
2007-08-19
05:00:32
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25 answers
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asked by
Anonymous
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Religion & Spirituality