Prime Numbers
prefixes  sieve
of Eratosthenes
Prime Numbers
A prime number is a number
which is only divisible by itself and 1.
The number 1 is not a prime number,
so the smallest prime number is 2.
2 is the only even prime number because all other even numbers can be
divided by 2.
Prime numbers are essential in modern cryptography.
Sieve of Eratosthenes
From Wikipedia:
In mathematics, the Sieve
of Eratosthenes
is a simple, ancient algorithm for finding all prime numbers up to a
specified integer. It works efficiently for the smaller primes (below
10 million). It was created by Eratosthenes, an ancient Greek mathematician.
The way it works is that when a prime number is found, all multiples of that prime number are eliminated.
The Sieve
of Eratosthenes is quite efficient because factors only need to be checked up to the square root of the maximum number in the sieve. (This point is also very useful for factorising numbers in general.) In the above grid, only the numbers 10 and under thus need to be checked, because 11^{2} = 121. Anything that has not been ruled out after these first few factors have been checked is a prime number.
Eratosthenes was a polymath – someone good at a large number of different things. He had many claims to fame, including being the first person to calculate the circumference of Earth. He was only 66 km out (0.16%), which is not bad at all for 240 BC. (Yes, the ancient Greeks not only knew Earth is round, but knew how big it is.)
