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
