Born to do Math 38 – Metaprimes (Part 4)
Author(s): Scott Douglas Jacobsen and Rick Rosner
Publication (Outlet/Website): Born To Do Math
Publication Date (yyyy/mm/dd): 2017/04/14
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Rick Rosner: You can’t have two sets of adjacent primes except 3, 5, and 7 because one of those numbers is going to be divisible by 3, but you can have two sets of twin primes with the middle one kind of missing out of 5 consecutive odd numbers like 11 and 13, and 17 and 19. There are a whole bunch of other things that kind of come off of this conjecture. That there is an infinity of primes that differ by 4 or differ by 6 or any kind of relationship like that.
Scott Douglas Jacobsen: That’s interesting. That’s interesting.
RR: I suspect, but have been too lazy and undereducated to do anything with it. That the way of setting up the primes via metaprimes. That is, that the numbers exist via their relationships among themselves prohibits prohibitive principles. That is, that there is not enough information. There’s just enough information to define the ratios among the various primes to infinite precision, but to set up a deal where there isn’t an infinity of twin primes would require superimposing more information on those ratios.
It would require a little extra cooking. I doubt there’s extra information among those ratios to shut down the twin prime business. All of those statements that there’s an infinity of these special primes will turn out to be true if they’re of that type because there’s not enough information in those ratios on the number line to plug the all of holes that you need to plug. So you make sure that every time you have a prime you don’t have another prime two steps down the number line.
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