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Find largest left truncatable prime in a given base: Difference between revisions

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Find largest left truncatable prime in a given base (view source)

Revision as of 10:27, 30 August 2013

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Putting "1" in front of a candiadate must result in a "1" first.
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m (Putting "1" in front of a candiadate must result in a "1" first.)
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A [[Truncatable primes|truncatable prime]] is one where all non-empty substrings that finish at the end of the number (right-substrings) are also primes ''when understood as numbers in a particular base''. The largest such prime in a given (integer) base is therefore computable, provided the base is larger than 2.
 
Let's consider what happens in base 10. Obviously the right most digit must be prime, so in base 10 candidates are 2,3,5,7. Putting a digit in the range 1 to base-1 in front of each candidate must result in a prime. So 212 and 515, like the whale and the petunias in ''The Hitchhiker's Guide to the Galaxy'', come into existance only to be extinguished before they have time to realize it. 13,17, ... 83,97 are candidates. Again, putting a digit in the range 1 to base-1 in front of each candidate must be a prime. Repeating until there are no larger candidates finds the largest left truncatable prime.
 
Let's work base 3 by hand:
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