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