Thread: Math trivia
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Old 12-26-2007, 09:58 PM
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Default Re: Math trivia

An interesting, though practically useless theorem, by Mills: It's often said that there isn't a formula for producing prime numbers. It may or may not be true that there isn't a practical formula that will produce prime numbers (though there are certainly simple algorithms which produce primes in a practical way).

Anyway, there is at least one formula that is proven to produce primes, though it is useless in practice as it relies on a 'seed' number which must be known to incredible accuracy. Our hero, who discovered this useless (as far as we know) formula in 1947, is one W. H. Mills. He proved there is a number, A, such that:

A3n is prime for all integer values of n.

Mills didn't even calculate a value for A - his proof showed that such a number must exist but didn't say what it was.

It has since been shown that there are an infinite number of possible values for A, the smallest of which is approximately 1.306377883863. This value generates an infinite series of primes beginning with 2, 11 and 1361.
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Dragar (12-29-2007)
 
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