A032734 All 81 combinations of prefixing and following a(n) by a single digit are nonprime.

2437, 5620, 7358, 11111, 13308, 13332, 13650, 14612, 19737, 19817, 24217, 25213, 26302, 27971, 28472, 28838, 29289, 29542, 29650, 31328, 33027, 33170, 35914, 35970, 36186, 37977, 38327, 39127, 39608, 40078, 41165, 41528, 42422, 43277, 44657, 45649, 47172, 47382

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• nice
• base

Examples

			2437 prefixed and followed with a pair of digits from (1,2,3,4,5,6,7,8,9) never yields a prime, e.g., '9'2437'1' = 7 * 37 * 43 * 83.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for primes involving decimal expansion of n

Crossrefs

Cf. A032682, A032683, A032684, A032685.

CF. A032702-A032733.

Programs

Maple

isA032734 := proc(n)
        for k from 1 to 9 do
        for k2 from 1 to 9 do
                dgs := [k,op(convert(n,base,10)),k2] ;
                dgsn := add( op(i,dgs)*10^(i-1),i=1..nops(dgs)) ;
                if isprime(dgsn) then
                        return false;
                end if;
        end do:
        end do:
        return true;
end proc:
for n from 1 to 50000 do
        if isA032734(n) then
                printf("%d,",n);
        end if;
end do: # R. J. Mathar, Oct 22 2011
filter:= proc(n) local d,i,j;
     d:= 10^(ilog10(n)+2);
     not ormap(isprime,[seq(seq(d*i+10*n+j,j=[1,3,5,7,9]),i=1..9)])
end proc:
select(filter,[$1..10^5]); # Robert Israel, Jul 07 2016

Mathematica

ok[n_] := With[{id = IntegerDigits[n]}, Select[ Flatten[ Table[ FromDigits[ Join[{j}, id, {k}]], {j, 1, 9}, {k, 1, 9}], 1], PrimeQ, 1] == {}]; A032734 = {}; n = 1; While[n < 50000, If[ok[n], Print[n]; AppendTo[A032734, n]]; n++]; A032734(* Jean-François Alcover, Nov 23 2011 *)
Select[Range[50000],NoneTrue[Flatten[Table[FromDigits[Join[{x}, IntegerDigits[ #],{y}]],{x,9},{y,9}]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 07 2018 *)

PARI

is_A032734(n)=p=10^#Str(n*=10);forstep(k=n+p,n+9*p,p,nextprime(k)>k+9 || return);1 \\ M. F. Hasler, Oct 22 2011

Python

from sympy import isprime
def ok(n):
    s, fdigs, edigs = str(n), "123456789", "1379"
    return not any(isprime(int(f+s+e)) for f in fdigs for e in edigs)
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Sep 05 2022