[HN Gopher] Right-Truncatable Prime Counter
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       Right-Truncatable Prime Counter
        
       Author : rainmans
       Score  : 8 points
       Date   : 2025-05-24 11:54 UTC (3 days ago)
        
 (HTM) web link (github.com)
 (TXT) w3m dump (github.com)
        
       | throwawaymaths wrote:
       | Curious about base 2. Obviously if you hit a 0 it's immediately
       | not prime, but maybe adjust the rules so:
       | 
       | - you drill through as many 0's on the right.
       | 
       | - you finish on 1.
       | 
       | 3, 5, 7, 11, 13, 15, 17 are all right truncatable, 19 is the
       | first non-truncatable prime in this scheme.
        
         | nh23423fefe wrote:
         | i dont think smaller radixes make the problem more interesting.
         | the problem is interesting because base 10 has a large
         | branching factor
        
           | throwawaymaths wrote:
           | I think in the base2 reformulation I propose we do not know
           | for certain if the list of numbers terminates, as all Fermat
           | primes are in the set and we don't know if there are
           | infinitely many Fermat primes.
           | 
           | For base-10 and the original rules the set is provably
           | closed.
           | 
           | "Drilling through zeros" makes the branching unbounded.
        
       | jinwoo68 wrote:
       | There's a Project Euler problem for finding truncatable prime
       | numbers, from both left and right:
       | https://projecteuler.net/problem=37
        
       | thechao wrote:
       | Just in case any else is wondering: there are only 83 right-
       | truncatable primes (RTP) and that is _it_. There 's two
       | constraints that let you see this "immediately":
       | 
       | 1. An RTP must start with {2,3,5,7,9}; and,
       | 
       | 2. An RTP must end with {1,3,7,9}.
       | 
       | So, let's take the largest RTP (73939133) and try to "extend" it:
       | there are only four possible extensions: 73939133[1],
       | 73939133[3], 73939133[7], 73939133[9]. None of these are prime.
       | This holds for the other 8-digit RTPs. Therefore, there is no
       | extension to a 9-or-longer RTP. Thus, the list is exhaustive.
        
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       (page generated 2025-05-27 23:02 UTC)