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%I #15 Mar 27 2023 09:48:56
%S 131,173,179,191,197,283,293,367,383,401,547,587,641,701,709,757,797,
%T 827,12197,12289,53881,54779,68927,37898818253
%N Full autoinsertable primes are such primes that remain prime after all the possible internal autoinsertions, one at a time.
%C Supposed to have only a finite quantity of terms. If the prime has K digits all the possible internal autoinsertions are K-1.
%C If it exists, the next term is > 2^32.
%e The prime 131 can be inserted into itself in two positions: 1'131'31, 13'131'1. Both are primes.
%e The prime 68927 can be inserted into itself in four positions: 6'68927'8927, 68'68927'927, 689'68927'27, 6892'68927'7. All the four are primes.
%o (PARI) forprime(p=11,10^8,my(v=digits(p),d=#v,f=1);for(i=1,d-1,my(t=concat(concat(v[1..i],v),v[i+1..d]),q=fromdigits(t));if(!isprime(q),f=0;break));if(f,print1(p,", "))) \\ _Hugo Pfoertner_, May 30 2020
%Y Cf. A247098.
%K nonn,base,more
%O 1,1
%A _Carlos Rivera_, May 29 2020
%E a(24) from _Michael S. Branicky_, Mar 27 2023
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