A217047 Primes that remain prime when a single "8" digit is inserted between any two adjacent digits.

11, 23, 47, 83, 131, 173, 179, 233, 353, 389, 521, 569, 641, 683, 839, 887, 911, 971, 983, 1229, 1289, 1913, 2087, 2663, 2837, 2879, 3329, 3671, 3677, 3803, 3821, 4259, 4409, 4817, 4871, 4889, 5237, 5477, 5693, 6449, 6581, 6863, 7283, 7487, 7583, 7823, 7853

Offset

1,1

Comments

These numbers are either isolated primes or the smaller of a pair of twin primes. - Davide Rotondo, Mar 11 2025

Links

Paolo P. Lava, Table of n, a(n) for n = 1..500

Example

325421 is prime and also 3254281, 3254821, 3258421, 3285421 and 3825421.

Maple

A217044:=proc(q, x) local a, b, c, d, i, k, n, ok, v; v:=[]; a:=10;
for n from 1 to q do a:=nextprime(a); d:=length(a); ok:=1;
for k from 1 to d-1 do b:=a mod 10^k; c:=trunc(a/10^k); i:=x*10^k+b; i:=c*10^length(i)+i;
if not isprime(i) then ok:=0; break; fi; od; if ok=1 then v:=[op(v), a]; fi; od; op(v); end:
A217044(10^3, 8);

Prog

(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
(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
(Python)
from sympy import isprime, primerange
def ok(p):
    if p < 10: return False
    s = str(p)
    return all(isprime(int(s[:i] + "8" + s[i:])) for i in range(1, len(s)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(7854)) # Michael S. Branicky, Nov 23 2021

Crossrefs

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217046, A217062-A217065.

Sequence in context: A282531 A309851 A145994 * A139834 A100558 A126199

Adjacent sequences: A217044 A217045 A217046 * A217048 A217049 A217050

Keyword

nonn,base

Author

Paolo P. Lava, Sep 25 2012

Status

approved