A335271 Full autoinsertable primes are such primes that remain prime after all the possible internal autoinsertions, one at a time.

131, 173, 179, 191, 197, 283, 293, 367, 383, 401, 547, 587, 641, 701, 709, 757, 797, 827, 12197, 12289, 53881, 54779, 68927, 37898818253

Offset: 1

Author

Carlos Rivera, May 29 2020

Keywords

• nonn
• base
• more

Comments

Supposed to have only a finite quantity of terms. If the prime has K digits all the possible internal autoinsertions are K-1.

If it exists, the next term is > 2^32.

Examples

			The prime 131 can be inserted into itself in two positions: 1'131'31, 13'131'1. Both are primes.
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.
		

Crossrefs

Cf. A247098.

Programs

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

Extensions

a(24) from Michael S. Branicky, Mar 27 2023