# [seqfan] Re: Pandigital primes in bases 8, 12, 16, 20, 36

Maximilian Hasler maximilian.hasler at gmail.com
Sat Mar 20 01:26:34 CET 2010

```Base 12 pandigital primes seem to start with
8989787252711, 8989787311891, 8989787313343, 8989787458763,
8989787707627, 8989787709211, 8989787710927, 8989788452371,
8989787959879, 8989787764211, 8989788261983, 8989787806099,
8989787992747, 8989788241699, 8989788262423, 8989787974883,
8989787810719, 8989788495007, 8989787999743, 8989788058351, ...

= "101234568A79B", "10123456B8A97", "10123456B98A7", "1012345769A8B",
"1012345869AB7", "101234586A9B7", "101234586B9A7", "1012345B68A97"...

Now I have a function for any base :)
pdp(b=12,c=20)={ my(t,offset,bp=vector(b,i,b^(b-i))~);
forstep(j=1,b-1,1, offset=b*(b^b-1)/(b-1)+j*b^b;
for(i=0,b!-1, isprime(t=offset-numtoperm(b,i)*bp) & !print1(t", ") &
!c-- & return))}

Hexa:
18528729602926047181, 18528729602926100221, 18528729602926234591,
18528729602926112701, 18528729602926235071, 18528729602926108411,
18528729602926116331, 18528729602927029471, 18528729602930170831,
18528729602928082621, 18528729602930167741, 18528729602928082411,...

= "10123456789ABEFCD", "10123456789ACBEFD", "10123456789AECBDF",
"10123456789ACEFBD", "10123456789AECDBF", "10123456789ACDEFB"....

base-20:
105148064265927977839670339, 105148064265927977839990337,
105148064265927977839838717, 105148064265927977848790339,
105148064265927977843159537, 105148064265927977846038379,
105148064265927977852278397, 105148064265927977848933979,
105148064265927977852157937, ...

= "10123456789ABCDEHIFGJ", "10123456789ABCDEJIFGH",
"10123456789ABCDEIJGFH", "10123456789ABCDHEIFGJ",...

base-36:
106474205747327721970821813283682888755465951838540182351,
106474205747327721970821813283682888755465951838655934631,
106474205747327721970821813283682888755465951838716447391,
106474205747327721970821813283682888755465951838776957771,
106474205747327721970821813283682888755465951838718031211,
106474205747327721970821813283682888755465951838781855251, ...

= "10123456789ABCDEFGHIJKLMNOPQRSTUXYZWV",
"10123456789ABCDEFGHIJKLMNOPQRSTWUVYXZ",
"10123456789ABCDEFGHIJKLMNOPQRSTXUWYVZ",
"10123456789ABCDEFGHIJKLMNOPQRSTYUXWZV", ...

Maximilian

> On Sat, Mar 20, 2010 at 12:02 AM, Alonso Del Arte
> <alonso.delarte at gmail.com> wrote:
>> If it interests anyone, I am slightly curious to find out a few pandigital
>> primes in bases 8, 12, 16, 20, 36. I just got done adding
>> http://oeis.org/wiki/Classifications_of_prime_numbers#By_representation_in_specific_bases
>> There
>> are other calculations I'm much more interested in, but I have to admit I do
>> care a tiny bit to know the answer to this one. There is also the
>> interesting issue of representing such large numbers in a compact manner. In
>> the case of the third vigesimal Smarandache-Wellin prime, I searched long
>> and hard for a concise way to express it in the form x^y - r, but to no
>> avail.
>>
>> Of the various sequences listed in that new section which are not already in
>> the OEIS as A-numbered sequences, the only one which I would consider worth
>> submitting is the sequence of binary Smarandache-Wellin primes, and even
>> that only after further study and after Neil's vacation. But if any of y'all
>> find anything interesting in the others, I hope you'd share it in this list.
>>
>> Al
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>

```