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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."
The reason - it's impossible to prove anything on an infinite set of data that isn't defined in the parameters of the data set.
This is not physics, in math u can easily prove theories involving infite data sets. Hello? irrational numbers? infitie series? they were all logically proven. Its *NOT* noteworthy because anyone can come up with these observations, but it takes a genius to prove it.
Great Atrocit
There, you've done it.
You've "easily" proven things by defining them as something. An irrational number is a number with no known, infinite, repeatable sequence? You've *defined* it that way, that doesn't mean you've ever *proven* a number irrational.
People are still doing work on Pi to see if it's got repeatable, discernable patterns someplace. The application of Logic does not prove things, proof cannot be generated with interpolation/extrapolation. 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). A Geometry proof, for instance, is an elegant placement of existing theorems to define a new one. "A works and B works and C works, therefore, D works." A Geometry *theorem* or *testable observation* is the creation of a new foundation that can be built from.
Of course they're noteworthy. Who are you to say that the editors of Nature don't know what to publish?
> 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"
In Mathematics, there's nothing that's "proven" that isn't explicitly defined as such. Notice how the Pythagorean Theorem is just that - a Theorem, not 'The Pythagorean Law'.
I don't see any difference between a "law" and a "theorem".
Anyway, a theorem is a formula that can be proven true.
Formulas that aren't theorems are, well, just formulas.
All the math we know consists of theorems, things that have been proven true. There are also some so-called "conjectures" - that means "we think this is a theorem but haven't found the proof yet.".
Experiments, hypotheses, data, tests, all that belongs to science - and math is not science.
I believe posters are recognized by their sig. So I made one.
Uh, I fail to see why this was moderated as interesting. "128 bit technology" ? I assume you are talking about symmetrical alg., like IDEA, CAST, and many others. These are not even remotely related to prime numbers (some of them are, but not very close). And it's already simple enough to generate big prime numbers.
Next step is to ask: "will my Diesel car become obsolete because of this theory" ?
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.