Problems & Puzzles: Puzzles

Puzzle 174. Primes & consecutive divisors

Here we will work with primes such that every left-section of the prime is exactly divided by the the quantity of digits of the section, except the whole prime, of course.

A small example is the prime 123259, because all the following are exact divisions:

1/1
12/2
123/3
1232/4
12325/5

Questions:
a) Find the largest prime of this kind
b) Find the largest number of this kind (here the exception does not apply)

Solution:

Jud McCranie, J. C. Colin and Joe K. Crump found the asked solutions:

a) 123 606 009 012 225 672 009 013 (24 digits)
b) 3 608 528 850 368 400 786 036 725 (25 digits) 

Congratulations to all of them!

***