A245878 Primes p such that p - d and p + d are also primes, where d is the smallest nonzero digit of p.

67, 607, 6977, 68897, 69067, 69997, 79867, 80677, 88867, 97967, 609607, 660067, 669667, 676987, 678767, 697687, 707677, 766867, 777677, 786697, 866087, 879667, 880667, 886987, 899687, 906707, 909767, 966997, 990967, 6069977, 6096907, 6097997, 6678877

Offset: 1

Author

Colin Barker, Aug 05 2014

Keywords

• nonn
• base
• look

Comments

Intersection of A245744 and A245745.

The smallest nonzero digit of a(n) is 6, and the least significant digit of a(n) is 7.

Examples

			The prime 607 is in the sequence because 607 - 6 = 601 and 607 + 6 = 613 are both primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A245742, A245743, A245744, A245745, A245877.

Programs

Maple

f:= proc(x) local L,i,y;
   L:= subs(1=6,2=7,3=8,4=9, convert(x,base,5));
   if not member(6,L) then return NULL fi;
   y:= add(L[i]*10^(i-1),i=1..nops(L));
   if isprime(y) and isprime(y-6) and isprime(y+6) then y else NULL fi
end proc:
map(f, [seq(2+5*k,k=1..10000)]); # Robert Israel, Nov 25 2024

Mathematica

pdQ[p_]:=Module[{c=Min[DeleteCases[IntegerDigits[p],0]]},AllTrue[p+{c,-c},PrimeQ]]; Select[Prime[Range[460000]],pdQ] (* Harvey P. Dale, Feb 26 2023 *)

PARI

s=[]; forprime(p=2, 7000000, v=vecsort(digits(p),,8); d=v[1+!v[1]]; if(isprime(p-d) && isprime(p+d), s=concat(s, p))); s

Python

from sympy import isprime
from sympy import prime
for n in range(1, 10**6):
  s=prime(n)
  lst = []
  for i in str(s):
    if i != '0':
      lst.append(int(i))
  if isprime(s+min(lst)) and isprime(s-min(lst)):
    print(s, end=', ')
# Derek Orr, Aug 13 2014