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

%I A344626 #12 Jun 30 2021 09:04:40
%S A344626 13,17,31,37,71,73,79,97,101,103,107,127,149,157,163,173,181,191,271,
%T A344626 277,307,313,317,331,359,367,379,397,419,479,491,571,577,593,617,631,
%U A344626 673,701,709,727,739,757,761,787,797,811,839,877,907,911,937,941,947,977
%N A344626 Primes p such that exactly two numbers among all circular permutations of the digits of p are prime.
%H A344626 Felix Fröhlich, <a href="/A344626/b344626.txt">Table of n, a(n) for n = 1..10000</a>
%o A344626 (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
%o A344626 eva(n) = subst(Pol(n), x, 10)
%o A344626 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)
%o A344626 forprime(p=1, 1e3, if(is(p), print1(p, ", ")))
%Y A344626 Cf. A270083. Row 2 of A317716.
%Y A344626 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).
%K A344626 nonn,base
%O A344626 1,1
%A A344626 _Felix Fröhlich_, May 25 2021