Since p: has a limit (why is that, by the way? I have written a pi(x) function using Miessel's formula in another language and it does grind to a slowdown for values much larger than 1e7, so that might be the reason. I'm assuming internally J uses Miessel or Lehmer's formula.), it might be better to "cheat" and just use a hardcoded value for pi(1e9).
https://primes.utm.edu/howmany.html (scroll down to table 1) Also, possibly the worst idea ever, why not iterate from 2 to 1e9 and do prime tests and keep a record of the previously found prime to compare the final digits with the next prime, and keep a record of the comparisons. Probably hopelessly slow, and inefficient. -------------------------------------------- On Tue, 3/22/16, Raul Miller <[email protected]> wrote: Subject: Re: [Jchat] primes To: "Chat forum" <[email protected]> Date: Tuesday, March 22, 2016, 12:14 AM Oh, I coded wrong. The limit error was from p:, but I should not have been feeding it the value 1e9. Sometimes I wonder how I get anything done... Thanks, -- Raul On Mon, Mar 21, 2016 at 11:03 AM, Roger Hui <[email protected]> wrote: > > it should be straightforward to do the extra credit problem > > I should have checked. The extra credit problem is for 100,000,000 primes. > > _1 p: _1+2^31 > 105097564 > p: 1e8 > 2038074751 > > So the limit error is not in p: . > > > > > > > On Sun, Mar 20, 2016 at 4:44 PM, Raul Miller <[email protected]> > wrote: > > > Rosettacode has a task now, for this item. > > > > http://rosettacode.org/wiki/Prime_conspiracy#J > > > > And, hypothetically speaking, it should be straightforward to do the > extra > > credit problem. But that doesn't work. Given: > > > > dgpairs=: 2 (,'->',])&":/\ 10 | p: > > combine=: ~.@[ ,.~ ' ',.~ ":@,.@(+//.) > > > > We can try this: > > > > /:~ combine&;/|: (~.;#/.~)@dgpairs@((+ i.)/)"1 > > (1e6*i.1e3),.1e6+999>i.1e3 > > > > |limit error: dgpairs > > > > ... but p: doesn't work for values like 1e9 (1 p: works, but not p: > > itself). > > > > And, for example, Roger has worked out some ways of dealing with large > > primes -- see looking at > > http://code.jsoftware.com/wiki/Essays/Primality_Tests -- but we don't > have > > anything that's a drop in replacement for the p: monad. > > > > So this presents something of a problem - how would we tackle a problem > > like this? > > > > (Please feel free to change forum to programming if you've got working > code > > rather than just ideas...). > > > > Thanks, > > > > -- > > Raul > > > > > > > > > > On Tue, Mar 15, 2016 at 7:02 AM, Cliff Reiter <[email protected]> > > wrote: > > > > > A look at the frequencies of pairs of last digits of successive primes: > > > /:~({.,#)/.~2]\10|p:4+i.1e7 > > > > > > 1 1 446808 > > > > > > 1 3 756071 > > > > > > 1 7 769924 > > > > > > 1 9 526953 > > > > > > 3 1 593196 > > > > > > 3 3 422302 > > > > > > 3 7 714795 > > > > > > 3 9 769915 > > > > > > 7 1 639383 > > > > > > 7 3 681759 > > > > > > 7 7 422289 > > > > > > 7 9 756852 > > > > > > 9 1 820369 > > > > > > 9 3 640076 > > > > > > 9 7 593275 > > > > > > 9 9 446032 > > > > > > The 1 follows 1 as rare as 9 follows 9, but rarer is 3 follows 3 as > rare > > > as 7 follows 7. 9 1 most popular! Very curious. Probably should move to > > > JProg' Best, Cliff > > > > > > > > > > > > > > > On 3/14/2016 12:03 PM, R.E. Boss 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
