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!

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