A college reader from the US (whom I shall generously leave nameless)
wrote saying he had read
my various maths pages
and liked in particular the pretty
quilt of prime numbers
I wrote about (Sieve of Eratosthenes page). Thanks. BUT!,
he then asked *What's the biggest prime?*

There is no biggest prime, sir. There are an infinite number
of primes. Remember, an integer is either itself prime or can be
uniquely factored into a product of primes.
So assume that there were a largest prime **P**.
Now form the product of all primes upto and including prime **P**, write
2*3*5*7*11*13.....*P = **N**.
Add one, giving **M=N+1**.
Now M is either prime or factorable. If it is prime, it is bigger than P,
thus leading to a contradiction. Assume it is factorable, then if you divide **M**
by any of the primes 2
through **P** there will always be a remainder (1) left over.
So **M** must have a factor larger than **P**, which is a contradiction again.
Therefore there is no largest prime **P**. *Quod erat demonstrandum!*

Now go visit my blog please, or look at other interesting maths stuff :-)

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