23 Jun
2004
23 Jun
'04
10:40 a.m.
=Paul R. Pudaite
=Robert Baillie The first 16208 digits of Pi are a probable prime. Could you also try digits of pi to other bases? Particularly base 2.
While we're asking: what about numbers *all* of whose initial strings are primes? Are there any? Infinitely many? In binary: obviously none since you can't even start with 0 or 1. In ternary: each choice is forced, and you can only get as far as "2122" = 71. If such exist: What is the smallest base? Is there a sharp lower bound on the number itself? If not: How far can you get in each base? (Nice sequence for OEIS, maybe?)