> .. 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.
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> .. 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.
Nice example. Here's another: https://secure.wikimedia.org/wikipedia/en/wiki/Magicicada
http://www.baltimoresun.com/bal-te.ms.cicada10may10,0,563814...