A344626 Primes p such that exactly two numbers among all circular permutations of the digits of p are prime.

13, 17, 31, 37, 71, 73, 79, 97, 101, 103, 107, 127, 149, 157, 163, 173, 181, 191, 271, 277, 307, 313, 317, 331, 359, 367, 379, 397, 419, 479, 491, 571, 577, 593, 617, 631, 673, 701, 709, 727, 739, 757, 761, 787, 797, 811, 839, 877, 907, 911, 937, 941, 947, 977

Offset: 1

Author

Felix Fröhlich, May 25 2021

Keywords

• nonn
• base

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A270083. Row 2 of A317716.

Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344627 (k=3), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Programs

PARI

rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==2, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))