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How far can you go? (Posted on 2011-03-04) Difficulty: 5 of 5
Starting with a prime digit add another digit, after or before the first, then another, adding it after, before or within the second number, and continue, keeping the resulting numbers prime, without repeating any of the digits you have used so far.

Example: 2, 23, 263, 2063, 29063....

Obviously you cannot reach a pandigital number (it will always be divisible by 9) .

What are the lowest and highest numbers in the set of eligible solutions with the maximum number of digits?

Please specify the interim stages leading to your results.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Smarandache-Wellin numbers? | Comment 10 of 11 |
(In reply to Smarandache-Wellin numbers? by Benny)

Not the same thing. For example, 2, 23, 235, 2357, 235711 adds two digits rather than one at the end.  Digits can be repeated as does the 1 here, and as 13 will be concatenated next, there'll be another 1 and another 3. New numbers are always added at the end and must be primes themselves. There's no choice involved--the next concatenation is determined by the next prime.
  Posted by Charlie on 2011-03-05 21:29:12

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