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
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
Programs
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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() */
Comments