A335314 Full autoinsertable of reversed multidigit primes are such primes that remain prime after all the possible internal autoinsertions of the reversed prime, one at a time.

127, 131, 149, 163, 191, 347, 383, 457, 463, 479, 521, 569, 571, 613, 643, 653, 659, 739, 757, 797, 941, 40471, 49991, 79627, 81869, 83407, 5916623

Offset: 1

Author

Carlos Rivera, Jun 01 2020

Keywords

• nonn
• base
• more

Comments

If the prime has K digits all the possible internal autoinsertions are K-1.

Supposed to have only a finite quantity of terms.

If it exists, the next term a(28) is > 2^32.

Examples

			Example: 127 generates 2 primes 1'721'27 and 12'721'7
Example: 5916623 generates 6 primes: 5'3266195'916623, 59'3266195'16623, 591'3266195'6623, 5916'3266195'623, 59166'3266195'23, 591662'3266195'3
		

Crossrefs

Cf. A335271.

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], Vecrev(v)), v[i+1..d]), q=fromdigits(t)); if(!isprime(q), f=0; break)); if(f, print1(p, ", "))) \\ Hugo Pfoertner, Jun 01 2020