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%I #21 Sep 08 2022 08:46:04
%S 11,23,47,83,131,173,179,233,353,389,521,569,641,683,839,887,911,971,
%T 983,1229,1289,1913,2087,2663,2837,2879,3329,3671,3677,3803,3821,4259,
%U 4409,4817,4871,4889,5237,5477,5693,6449,6581,6863,7283,7487,7583,7823,7853
%N Primes that remain prime when a single "8" digit is inserted between any two adjacent digits.
%H Paolo P. Lava, <a href="/A217047/b217047.txt">Table of n, a(n) for n = 1..200</a>
%e 325421 is prime and also 3254281, 3254821, 3258421, 3285421 and 3825421.
%p with(numtheory);
%p A217044:=proc(q,x)
%p local a,b,c,i,n,ok;
%p for n from 5 to q do
%p a:=ithprime(n); b:=0;
%p while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;
%p for i from 1 to b-1 do
%p c:=a+9*10^i*trunc(a/10^i)+10^i*x;
%p if not isprime(c) then ok:=0; break; fi; od;
%p if ok=1 then print(ithprime(n)); fi;
%p od; end:
%p A217044(100000,8)
%o (PARI) is(n)=my(v=concat([""],digits(n)));for(i=2,#v-1,v[1]=Str(v[1], v[i]); v[i]=8;if(i>2,v[i-1]="");if(!isprime(eval(concat(v))), return(0)));isprime(n) \\ _Charles R Greathouse IV_, Sep 25 2012
%o (Magma) [p: p in PrimesInInterval(11,8000) | forall{m: t in [1..#Intseq(p)-1] | IsPrime(m) where m is (Floor(p/10^t)*10+8)*10^t+p mod 10^t}]; // _Bruno Berselli_, Sep 26 2012
%o (Python)
%o from sympy import isprime, primerange
%o def ok(p):
%o if p < 10: return False
%o s = str(p)
%o return all(isprime(int(s[:i] + "8" + s[i:])) for i in range(1, len(s)))
%o def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
%o print(aupto(7854)) # _Michael S. Branicky_, Nov 23 2021
%Y Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217046, A217062-A217065.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Sep 25 2012
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