Born to do Math 37 – Metaprimes (Part 3)
Author(s): Scott Douglas Jacobsen and Rick Rosner
Publication (Outlet/Website): Born To Do Math
Publication Date (yyyy/mm/dd): 2017/04/13
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Scott Douglas Jacobsen: As you know, math assumes axioms. So this is assuming some axioms. So one that comes to mind—well, even before that, when you’re talking about – as a premise to this appendix to the previous discussion. It was codeless information in the universe with an example to metaprimes and the axioms that are being assumed here are a) the prime sequences and b) [Laughing] the metaprime sequences implied within that.
So it is not necessarily codeless. Is it? Or if it isn’t, how?
Rick Rosner: I’m not saying that it is. I am saying it is a way of defining words by their relationships to each other, via the integers and their relationships to one another. I would think it has implications in terms of things like the Twin Prime Theorem, which is that – or postulates. It is not a theorem. It postulates that there are a limited number of primes that differ only by 2, like 3 and 5, 5 and 7, 11 and 13, 29 and 31.
SDJ: Is it the Twin Prime Conjecture? It is just coming to me now.
RR: Theorem, Conjecture, sorry. There’s no biggest pair of twin primes. You can always find a biggest pair, which is the same as saying there’s an infinity of them. You can’t – to be clear—there’s only one set of primes that differ by 1, which is 2 and 3. There are no more primes that differ by 1. That would require one of those numbers to be even and each of those numbers is divisible by 2.
But you can have a bunch of numbers. People conjecture that there is an infinity of them that differ by 2: 100 and 103, you can’t have 3 in the row except for 3, 5, and 7.
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