Tuesday, April 18, 2006


Prime rules and extreme mathematics

Relying on my prime counting function I have some interesting rules governing primes, where it took a couple of days to them right!!!

Given a prime p, if p+1 has 3 as a factor, then p+2 is either prime or equals a prime squared.

If instead p-1 has 3 as a factor, then either p-2 is prime, or it factors into exactly two primes, or at least one factor of p-2 must be less than p^{1/3}.

Those are the correct set of prime rules, and it took me a couple of days to figure them out, where with the p-1 case it was a major mess.

But that's the discovery process! It's messy.

And part of extreme mathematics as I practice it is letting people in on the full discovery process, including the mistakes and failed arguments, along with the mirages, where you think you're right, but you're wrong!

Test the rules. It is extreme mathematics so maybe I missed something, but as these iterations go through that gets less and less likely.

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