OFFSET
1,1
COMMENTS
The basic rule is: if no substring of p matches any smaller prime of the form 4n+3, add p to the list. The basic theorem of minimal sets says that the minimal set is always finite.
The sequence b-file is complete except for the number (2*10^19153 + 691)/9, i.e., the decimal number consisting of 19151 "2"s followed by two "9"s. - Curtis Bright, Jan 23 2015
LINKS
Walter A. Kehowski and Curtis Bright, Table of n, a(n) for n = 1..112 (first 103 terms from Walter A. Kehowski)
Walter A. Kehowski, Full list of terms
F. Morain, Primality certificate for the largest number of A111056, May 4 2015.
Carlos Rivera, Puzzle 178. Shallit Minimal Primes Set, The Prime Puzzles & Problems Connection.
Jeffrey Shallit, Minimal primes, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 1999-2000.
EXAMPLE
From Danny Rorabaugh, Mar 26 2015: (Start)
a(5) is not 23, even though 23 is the fifth prime of the form 4n+3, since 23 contains a(1)=3 as a substring. Similarly: 31 and 43 contain 3 and 47 contains a(2)=7. Thus a(5)=59.
This sequence contains 2099 since 2, 0, 9, 20, 09, 99, 209, 299, and 099 are not primes of the form 4n+3.
(End)
MAPLE
with(StringTools); wc := proc(s) cat("*", Join(convert(s, list), "*"), "*") end; M3:=[]: wcM3:=[]: p:=1: for z from 1 to 1 do for k while p<10^11 do p:=nextprime(p); if k mod 100000 = 0 then print(k, p, evalf((time()-st)/60, 4)) fi; if p mod 4 = 3 then sp:=convert(p, string); if andmap(proc(w) not(WildcardMatch(w, sp)) end, wcM3) then M3:=[op(M3), p]; wcM3:=[op(wcM3), wc(sp)]; print(p) fi fi od od; # Let it run for a couple of days.
CROSSREFS
KEYWORD
base,fini,nonn,uned,changed
AUTHOR
Walter Kehowski, Oct 06 2005
STATUS
approved