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Prime Numbers Not So Random?
Jeff Moriarty writes "Some physicists believe they might have caught a whiff of a pattern in the sequence of prime numbers. This would have a huge impact across mathematics, and to people who just really like primes... or like being Prime."
> In the scientific community, proof is established by repeated experimental repetition, in Mathematics, testing this theory lots of times with lots of different numbers (see computers)
Sorry. Say that to a mathematician, and see how he laughs at you, or kicks you out.
A theorem is statement which can be verified by mathematical operations.
The statements usually includes axioms, which are not provable, and which define the mathematical operations on the given problem. The only thing you have to do is show is, given these axioms, the statement is always true.
The sequence of application of axioms is called "proof".
And mathematicians are very peculiar with "always". For scientists "always" means "many times, and until some shows otherwise", because you can't define these axioms.
Mathematics is not the kind of science you are thinking of. You are thinking of natural science.
In mathematics, humans define the axioms. They may, or may not bear any relationship to reality.
It some aspects, it resembles more philosophy than physics.
> Who are you to say that the editors of Nature don't know what to publish?
Probably a mathematician. They don't give a lot on physicists saying, "Hey, by finding some statistical correlation, we found a pattern, which holds true, in our finite data set, most of the time".
"Between strong and weak, between rich and poor [...], it is freedom which oppresses and the law which sets free"
Of course they are prime ! ANY number is either:
6n (not prime of course)
6n+1
6n+2 (not prime of course)
6n+3 (not prime of course)
6n+4 (not prime of course)
6n+5
And 6n+5 is the same as 6(n+1)-1 so indeed you are right. You deserve a price for finding a 6th grade theorem.