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.

(In reply to Smarandache-Wellin numbers? by Benny)

From what I understand of the Wiki page the S-W numbers are the successive concatenation of primes,
2
2 + 3  → 23
23 + 5 → 235
235 + 7 → 2357
2357 + 11 → 235711
235711 + 13 → 23571113

This is not what Ady was asking, concatenation yes, but one often needs to split the previous number in order to insert the next prime.

Posted by brianjn on 2011-03-05 19:54:28