|The ancients Greeks were switched on dudes |
It amazes me how advanced the Ancient Greek's were in mathematics. About 2000 years ago, they had the most impressive library in Ancient History, the Library of Alexandria. The library also had a large museum, and zoo. It also had housing for researchers who lived there in the library with their families while they did their research. Archimedes, and Euclid are a few famous mathematicians who studied there.
Euclid proved that there is an infinite amount of prime numbers. The proof is like this:
Make a list if prime numbers , : 2, 3, 5, 7 ... P(n). Let P be the product of the terms p(1) thought P(n), plus 1.
P = (2 * 3 * 5 * ... * P(n)) + 1
If the sum is prime, then you have a prime number greater than any primes in the list.
If P is not prime then, like all integers, it must have a unique prime factorization; and so it must be divisible by a prime number.
But it cannot be any primes in the list because
P mod (any of the primes in that list ) = 1
So there exists some prime not in your list.