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

17773937, 39371777, 71777393, 73937177, 77393717, 77739371, 93717773, 101717933, 101793137, 111766999, 111897767, 113379997, 113719261, 113773021, 113913133, 117669991, 118977671, 119307977, 119937137, 123975113, 131239751, 131331139, 131473193, 133113913

Offset: 1

Author

Felix Fröhlich, May 25 2021

Keywords

• nonn
• base

Crossrefs

Cf. A270083. Row 7 of A317716.

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).

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==7, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))