|
|
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.
|
|
0
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
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
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|