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

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

Revision as of 13:45, 1 September 2013

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Undo revision 167123 by Bengt (talk) 2 is eliminated because 12 22 32 42 52 62 72 82 and 92 are not prime, not because 12 is not. Similarly for 3. Maybe what exists is unclear but this is not the change

Nigel Galloway

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Revision as of 10:27, 30 August 2013 (view source) rosettacode>Bengt m (Putting "1" in front of a candiadate must result in a "1" first.) ← Older edit		Revision as of 13:45, 1 September 2013 (view source) Nigel Galloway (talk \| contribs) (Undo revision 167123 by Bengt (talk) 2 is eliminated because 12 22 32 42 52 62 72 82 and 92 are not prime, not because 12 is not. Similarly for 3. Maybe what exists is unclear but this is not the change) Newer edit →
Line 2: 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 122 and 155, 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: