On Wed, 23 Jun 2004, Marc LeBrun wrote:
While we're asking: what about numbers *all* of whose initial strings are primes?
Are there any? Infinitely many?
Yes, there are just a finite number of both types (all initial strings are prime or all terminal strings are prime). See http://mathworld.wolfram.com/TruncatablePrime.html Just about any question of this type that one can ask has been examined by prime enthusiasts. The only problem is finding out what they have been named. In this case it is left or right truncatable prime and undoubtedly others have looked at them and given them other names. I heard about these primes from John Maxfield back in 1966 or so, but had a problem locating this reference. Finally I found it by going to mathworld and looking thru all entries returned by a search on primes. Speaking of truncation, the MathWorld entry mentions a similar class of primes called "Henry VIII primes".:-) --Edwin