Which Was What We Wanted. The abbreviation WWWWW
may be placed at the end of a mathematical
proof to serve a similar purpose as
QED.
We will prove by reductio
ad absurdum that there are infinitely many primes.
Assume the opposite, that there are exactly n primes. Let
set S contain all n primes in increasing order, such that S={X1, X2, X3... Xn}.
Consider
Y such that Y=1+(X1*X2*X3*...*Xn)
Y gives a remainder of 1 when divided by any element of S. Hence Y is not divisible by any
prime and must be a
prime itself.
Yet this contradicts the assumption that there are only n primes, as the existence of Y means there must be at least n+1 primes.
The assumption must then be false and there must be infinitely many primes.
WWWWW.