Of course, the observations noted in that quantamagazine article were also based on a finite batch of "small" primes.
And a lot of this seems to boil down to 2 and 3 being prime numbers, together occupying a significant chunk of the Sieve of Eratosthenes. -- Raul On Mon, Mar 14, 2016 at 9:37 PM, Don Guinn <[email protected]> wrote: > I > didn't > mean to draw any conclusions from that. It was just and interesting > observation. Why do multiples of six mean anything. I don't know. Maybe > they don't and the pattern will disappear with more primes. But it's > curious. > > On Mar 14, 2016 6:06 PM, "Roger Hui" <[email protected]> wrote: > >> You can not draw profound conclusions from a short initial segment of the >> primes. See for example Studio|Demos|Plot|Gallery|Prime Race. The plot is >> for primerace i.n where primerace=: [: +/\ _2 + 4 | p: , the number of >> primes that are 3 mod 4 minus the number of primes that are 1 mod 4. I >> believe there's a proof that the x-axis is crossed infinitely often, but >> you can't tell that by looking at the graph even for large n. >> >> >> On Mon, Mar 14, 2016 at 4:24 PM, Don Guinn <[email protected]> wrote: >> >> > And here is the grouping for last digits. Looks like 0 difference is >> about >> > even with a difference of 8 and loses out to 2 4 and 6. >> > >> > /:~(~.d),.#/.~d=.10|2-~/\p:i.10000000 >> > 0 1737431 >> > 1 1 >> > 2 2333292 >> > 4 1994255 >> > 6 2221597 >> > 8 1713423 >> > >> > But looking at the first list (in the previous post) there is a spike in >> > the count for multiples of 6 difference. Weird! >> > >> > On Mon, Mar 14, 2016 at 5:05 PM, Don Guinn <[email protected]> wrote: >> > >> > > Just played with the various spacing of primes and saw something a >> little >> > > odd. The number of primes differing by 6 are much larger than any other >> > > difference. (I know, the code is not efficient, but it is fast enough >> to >> > > play with.) >> > > >> > > 20{./:~(~.d),.#/.~d=.2-~/\p:i.10000000 >> > > 1 1 >> > > 2 738597 >> > > 4 738717 >> > > 6 1297540 >> > > 8 566151 >> > > 10 729808 >> > > 12 920661 >> > > 14 503524 >> > > 16 371677 >> > > 18 667734 >> > > 20 354267 >> > > 22 307230 >> > > 24 453215 >> > > 26 211203 >> > > 28 229177 >> > > 30 398713 >> > > 32 123123 >> > > 34 129043 >> > > 36 206722 >> > > 38 94682 >> > > >> > > >> > > On Mon, Mar 14, 2016 at 10:03 AM, R.E. Boss <[email protected]> >> > wrote: >> > > >> > >> >> > >> >> > >> https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/ >> > >> >> > >> >> > >> R.E. Boss >> > >> ---------------------------------------------------------------------- >> > >> For information about J forums see >> http://www.jsoftware.com/forums.htm >> > > >> > > >> > > >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> > >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
