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
> > ----------------------------------------------------------------------
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> >
> ----------------------------------------------------------------------
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