Prime Numbers
By: Joe Faletti
Prime numbers were first studied by ancient Greek
mathematicians. Euclid proved there are infinitely many primes
numbers. He also gave proof that every integer can be written as a
product of primes in a unique way.
Euler showed perfect prime of all even numbers with
2n-1 and 2n-1. It is not known if there are any odd perfect numbers.
In about 200 B.C Eratasthenes devised calculating primes
called the Sieve of Eratasthenes. There is not much history of prime
numbers during the Dark Ages.
In the 17th century Fermat proved that every prime number
of the form 4n+1 can be written as the sum of two squares and how
any number could be written as a sum of four squares. He devised a new
method of factoring large numbers . (Fermat's little theorem- a p=a
module p)
The equation 2n-1 was thought to prove a number prime
until Euler showed 232+1= 4294967297 is divisible by 641 so
it is not prime. The form 2n-1 was also proven that the result would
not always be prime.
Sourses:
http://www-groups.doc.st-and.ac.uk/~history/HistTopics/Prime_numbers.html
