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A344631 Primes p such that exactly seven numbers among all circular permutations of the digits of p are prime.

%I A344631 #7 May 26 2021 02:31:34
%S A344631 17773937,39371777,71777393,73937177,77393717,77739371,93717773,
%T A344631 101717933,101793137,111766999,111897767,113379997,113719261,
%U A344631 113773021,113913133,117669991,118977671,119307977,119937137,123975113,131239751,131331139,131473193,133113913
%N A344631 Primes p such that exactly seven numbers among all circular permutations of the digits of p are prime.
%o A344631 (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 A344631 eva(n) = subst(Pol(n), x, 10)
%o A344631 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==7, 1, 0)
%o A344631 forprime(p=1, 1e3, if(is(p), print1(p, ", ")))
%Y A344631 Cf. A270083. Row 7 of A317716.
%Y A344631 Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344627 (k=3), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344632 (k=8).
%K A344631 nonn,base
%O A344631 1,1
%A A344631 _Felix Fröhlich_, May 25 2021