Problems & Puzzles: Puzzles
Puzzle 157. Zip primes
Walter Schneider posts the following puzzle:
the number into k parts by alternately distributing the left-most digit to the parts.
For the number 27239 for example the zipping goes as follows:
k=2: 229 prime
k=3: 23 prime
k=4: 29 prime
We call a n-digit number N k-zippable (k=1,...,n) if
all k parts are prime. If this is true for k=1,2,...,K we
call N a zip prime of order K. If K is maximal (i.e.
K=n) we say N is a perfect zip
The example above shows that 27239 is a zip prime of
1. Show that there are only a finite quantity of perfect zip primes and obtain all of them.
2. Find five zip primes of
3. Find a zip prime
of order 8, 9 and 10.
Sudipta Das sent (October 29, 2002) the following answers to this puzzle. After this we only need a zip prime of order 9 & 10