Using your Head is Permitted

June 2012 riddle

Define a "lucky" number in base b to be a natural whose base b representation contains only digits that are either primes or are 1, and which satisfies that any consecutive substring of its digits is also a prime (or the number 1) in base b.

Is there any b for which there are an infinite number of base b lucky numbers?

List of solvers:

Joseph DeVincentis (2 June 06:09)
Lu Wang (2 June 22:43)
Radu-Alexandru Todor (3 June 07:04)
Wenqi Zhang (3 June 17:43)
Jan Fricke (5 June 08:08)
Djinn Lu (5 June 22:36)
Oded Margalit (7 June 15:11)
Christian Pape (10 June 0:03)
Dharmadeep Muppalla (10 June 11:39)
Itsik Horovitz (17 June 20:53)
Albert Stadler (20 June 20:34)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


To solution

Back to main page