A168169 Primes with d digits (d>0) which have more than 2d distinct primes as substrings.

23719, 31379, 52379, 113171, 113173, 113797, 123719, 153137, 179719, 199739, 211373, 213173, 229373, 231197, 231379, 233113, 233713, 236779, 237331, 237619, 237971, 241973, 259397, 291373, 313739, 317971, 327193, 337397, 343373, 353173

Offset: 1

Author

M. F. Hasler, Nov 28 2009

Keywords

• nonn
• base

Comments

"Substrings" includes the whole number in itself.

This is a subsequence of A168167.

The least palindrome in this sequence is 9179719.

Examples

			The least number with d digits to have over 2d distinct prime substrings is the prime a(1)=23719, with 5 digits and #{2, 3, 7, 19, 23, 37, 71, 719, 2371, 3719, 23719} = 11.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A093301, A069490, A131648, A012884, A168167, A168168.

Programs

Maple

filter:= proc(n) local i,j,count,d,S,x,y;
  if not isprime(n) then return false fi;
  d:= ilog10(n)+1;
  count:= 0; S:= {};
  for i from 0 to d-1 do
    x:= floor(n/10^i);
    for j from i to d-1 do
      y:= x mod 10^(j-i+1);
      if not member(y,S) and isprime(y) then count:= count+1; S:= S union {y}; if count > 2*d then return true fi fi
  od od;
  false
end proc:
select(filter, [seq(i,i=1..10^6,2)]); # Robert Israel, Nov 11 2020

PARI

{forprime( p=1, default(primelimit), #prime_substrings(p) > #Str(p)*2 & print1(p", "))} /* see A168168 for prime_substrings() */