Inspired by a Numberphile video on the topic, I wanted to personally investigate an algorithmic approach to finding numbers with high multiplicative persistence.

Multiplicative persistence: multiply the digits of the number together. The product is your new number. Example: 77 -> 49 -> 36 -> 18 -> 8. Four steps to reach a fixed point.

This is sequence A003001 in the On-Line Encyclopedia of Integer Sequences.

It is conjectured that there are no numbers of multiplicative persistence > 11.

The code uses a depth-first search technique (through recursion) looking for numbers which have a prime factorization composed entirely of 2s, 3s, and 7s.

These early attempts suggest that this might not be an efficient way to search for these numbers.

Potential improvements:

• parallelization
• other base systems