.. and it's only with their (relatively recent) use in cryptography that prime numbers became "important". G.H. Hardy, one of the leading number theorist in his era claimed that none of his work was useful, and therefore never could be applied to good or evil.
Makes you wonder what applications the future holds for what is considered purely theoretical today.
Primes are the "atomic" blocks of the natural numbers. Given the prime factors of a set of natural numbers, you can trivially computer the greatest common divisor and least common multiple. Primes are extremely important.
> .. and it's only with their (relatively recent) use in cryptography that prime numbers became "important".
A pair of mechanical gears with relatively prime numbers of teeth have a longer service life: a given tooth rubs the same amount against every tooth in the partner gear. If they are not relatively prime, the hardest tooth would hit only a few teeth on the partner gear, wearing them out many times faster.
