please excuse my previous reply, it seems I got the problem wrong :). My pseudo solution lists all primes that have any permutation being prime as well, rather than having all permutations being prime. It would require a step of checking that all permutations are present...
Jan-Pieter On Sat, 23 Sept 2023, 09:13 Jan-Pieter Jacobs, <janpieter.jac...@gmail.com> wrote: > I would tackle it like this: > > primegroups =: (#~1<#&>)(</.~ <@(/:~)@(10&#.inv)"0) i.&.(p: inv) 1e6 > > which starts from the list of primes under 1e6: i.&.(p:^:_1) 1e6 > > box those keyed by unique sets of digits: > > (</.~ <@(/:~)@(10&#.inv)"0) > > and finally remove primes that are alone in their box: > > (#~ 1<#&>) > > It looks like there are 4181 of such groups, with a total of 78160 primes. > > > Jan-Pieter > > On Sat, 23 Sept 2023, 07:54 'Skip Cave' via Programming, < > programm...@jsoftware.com> wrote: > >> Here's a verb p(n) to produce all n-digit primes with the same digits: >> >> odo=:#: i.@(*/) >> >> p=:{{(#~1&p:)10#.(odo y#4){1 3 7 9}} >> >> >> try it: >> >> p 2 >> >> 11 13 17 19 31 37 71 73 79 97 >> >> p 3 >> >> 113 131 137 139 173 179 191 193 197 199 311 313 317 331 337 373 379 397 >> 719 >> 733 739 773 797 911 919 937 971 977 991 997 >> >> p 4 >> >> 1117 1171 1193 1319 1373 1399 1733 1777 1913 1931 1933 1973 1979 1993 1997 >> 1999 3119 3137 3191 3313 3319 3331 3371 3373 3391 3719 3733 3739 3779 3793 >> 3797 3911 3917 3919 3931 7177 7193 7331 7333 7393 7717 7793 7919 7933 7937 >> 7993 9133 9137 9173 9199 9311 9319 9337 9371 9377 9391 9397 9719 9733 9739 >> 9791 9931 9973 >> >> p 5 >> >> 11113 11117 11119 11131 11171 11173 11177 11197 11311 11317 11393 11399 >> 11717 11719 11731 11777 11779 11933 11939 11971 13171 13177 13313 13331 >> 13337 13339 13397 13399 13711 13799 13913 13931 13933 13997 13999 17117 >> 17137 17191 17317 17333 17377 17393 17713 17737 17791 17911 17939 17971 >> 17977 19139 19319 19333 19373 19379 19391 19717 19739 19777 19793 19913 >> 19919 19937 19973 19979 19991 19993 19997 31139 31177 31193 31319 31333 >> 31337 31379 31391 31393 31397 31771 31793 31799 31973 31991 33113 33119 >> 33179 33191 33199 33311 33317 33331 33377 33391 33713 33739 33773 33791 >> 33797 33911 33931 33937 33997 37117 37139 37171 37199 37313 37337 37339 >> 37379 37397 37717 37799 37991 37993 37997 39113 39119 39133 39139 39191 >> 39199 39313 39317 39371 39373 39397 39719 39733 39779 39791 39799 39937 >> 39971 39979 71119 71171 71191 71317 71333 71339 71399 71711 71713 71719 >> 71777 71917 71933 71971 71993 71999 73133 73331 73379 73771 73939 73973 >> 73999 77137 77171 77191 77317 77339 77377 77711 77713 77719 77731 77773 >> 77797 77933 77977 77999 79111 79133 79139 79193 79319 79333 79337 79379 >> 79393 79397 79399 79777 79939 79973 79979 79997 79999 91139 91193 91199 >> 91331 91373 91393 91397 91711 91733 91771 91939 91997 93113 93131 93133 >> 93139 93179 93199 93319 93337 93371 93377 93719 93739 93911 93913 93937 >> 93971 93979 93997 97117 97171 97177 97373 97379 97397 97711 97771 97777 >> 97919 97931 97973 99119 99131 99133 99137 99139 99173 99191 99317 99371 >> 99377 99391 99397 99713 99719 99733 99793 99971 99991 >> >> Skip Cave >> Cave Consulting LLC >> >> >> On Sat, Sep 23, 2023 at 12:26 AM Richard Donovan <rsdono...@hotmail.com> >> wrote: >> >> > Hi >> > >> > I am trying to develop a program to find primes with n digits abc such >> > that acb bac bca cab and cba are also primes. (obviously trivial if aaa >> is >> > prime!). >> > >> > An example with n=3 is >> > >> > 1 p: 199 919 991 >> > >> > 1 1 1 >> > >> > These primes are thin on the ground since they cannot contain any of the >> > digits 2 4 5 6 8 or 0 and I am wondering if it would be best to >> construct >> > numbers omitting those containing those prohibited digits, or test every >> > comination of p: i. n which seems wasteful, especially since I want to >> find >> > all such primes below one million. >> > >> > Can anyone see an efficent way to produce this? >> > >> > Thanks in advance, >> > >> > Richard >> > ---------------------------------------------------------------------- >> > 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