| Grieve"s Twin Prime Conjecture | |
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14 Mar 2010 @ 11:50, by John Grieve
Points of Symmetry/ Work in Progress
Goldbach's Conjecture which states that all even numbers greater than 6 can be expressed as the sum of two odd primes, implies that every number greater than 3 is equidistant from two odd primes.( For example, if 20 equals 7 13 then 10 is equidistant from 7 and 13).
This of course applies to prime numbers themselves, so we can say (if Goldbach is correct) that every prime number greater than 3 is equidistant from two other prime numbers.
This raises an interesting possibility which seems to be confirmed by the facts. Every pair of twin primes that I have checked is equidistant from two other pairs of twin primes. For example, 11,13 is equidistant from 5,7 and 17,19. A larger example; 419,421 is equidistant from 239,241 and 599,601.
This suggests both that the Goldbach conjecture is true and also that there are an infinite number of twin primes, since any pair can be considered to be intermediate between greater and lesser pairs of twin primes.
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Category: Articles
1 comment
3 Apr 2010 @ 19:34 by : I've heard,
"It's all in the numbers."
I'm putting this on my "back-burner" in relation to the electromagnetic spectrum, the periodic chart, tones, and octaves.
This is very interesting!
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