Ooh, that's interesting... I wonder what other sequences do...?pic.twitter.com/YcjxD00OLz
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Ooh, that's interesting... I wonder what other sequences do...?pic.twitter.com/YcjxD00OLz
The 0-2 dynamics is apparently Wolfram's rule 90, preserving the 1. So the real challenge is to prove that the extended dynamics due to other numbers in the initial transient never manages to persist. Could well be halting-complete.pic.twitter.com/ac6m4cGH1Q
All prime numbers after 2 are odd. The 1 falls out of prime numbers being (1 + two times a number). so I’ll go look up Gilbreath’s conjecture and see why you can’t prove this...
All differences except column 1 are even, but they can be quite large for large primes. A proof would require to show that the differences per iteration in the matrix shrink faster than the differences between adjacent primes grow. Experimentally it looks true.
I have a proof but it is too large to fit in this tweet.
Kind of makes you want to re examine the argument that 1 is not prime.
If 1 were considered prime, the left edge would alternate 1 & 0 after the initial row. It wouldn't be all 1s. Or maybe I missed your point?
Adept at bowling, Clyde Hough-Remington (1952-1919) set up pins with these numbers at an alley in Wolverhampton in 1889. It took 19 attempts to knock down all pins save those on the left side. “Proven!” he exclaimed.
Apparently, Paul Erdős speculated that Gilbreath’s conjecture is true but it would be 200 years before anyone could prove it.https://mathoverflow.net/questions/34669/is-there-any-progress-toward-solving-gilbreaths-conjecture …
At any mention of Paul Erdős, I am obliged to cite his great quotation: "A mathematician is a device for turning coffee into theorems."
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