%I #22 Mar 08 2024 11:59:05

%S 11,17,19,23,29,31,37,41,43,61,73,79,89,97,101,103,127,167,173,181,

%T 211,233,239,251,271,283,307,331,359,373,439,491,509,523,547,599,673,

%U 709,733,769,877,887,937,941,991,1033,1229,1381,1619,1721,1759,1789,1901

%N Primes that remain prime when a single "3" digit is inserted between any two adjacent decimal digits.

%H Bruno Berselli, <a href="/A217063/b217063.txt">Table of n, a(n) for n = 1..1000</a> (first 275 terms from Paolo Lava)

%e 212881 is prime and also 2128831, 2128381, 2123881, 213288 and 2312881.

%p with(numtheory);

%p A217063:=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; 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; if not isprime(c) then ok:=0; break; fi; od;

%p if ok=1 then print(ithprime(n)); fi; od; end:

%p A217063(1000000,3);

%o (Magma) [p: p in PrimesInInterval(11, 2000) | forall{m: t in [1..#Intseq(p)-1] | IsPrime(m) where m is (Floor(p/10^t)*10+3)*10^t+p mod 10^t}]; // _Bruno Berselli_, Sep 26 2012

%o (PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=3; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ _Charles R Greathouse IV_, 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] + "3" + 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(1901)) # _Michael S. Branicky_, Nov 17 2021

%Y Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217047, A217062-A217065.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Sep 26 2012