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%I #15 Mar 30 2023 10:24:25
%S 113,131,197,199,311,337,373,719,733,919,971,991,1031,1091,1097,1103,
%T 1109,1123,1181,1213,1231,1279,1297,1301,1319,1327,1579,1777,1811,
%U 1873,1913,1949,1951,1979,1987,1993,2131,2311,2377,2399,2713,2791,2939,2971,3011
%N Primes p such that exactly three numbers among all circular permutations of the digits of p are prime.
%H Felix Fröhlich, <a href="/A344627/b344627.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Prime[Range[500]],Total[Boole[PrimeQ[FromDigits/@ Table[ RotateRight[ IntegerDigits[#],n],{n,IntegerLength[#]}]]]]==3&] (* _Harvey P. Dale_, Mar 30 2023 *)
%o (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 eva(n) = subst(Pol(n), x, 10)
%o 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==3, 1, 0)
%o forprime(p=1, 1e3, if(is(p), print1(p, ", ")))
%Y Cf. A270083. Row 3 of A317716.
%Y Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).
%K nonn,base
%O 1,1
%A _Felix Fröhlich_, May 25 2021
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