[crondee]

I dont think it will max out. I brute forced it upto 10 million and I got the following numbers (5, 679) (6, 6788) (7, 68889) (8, 2677889) sure the numbers are exponential but no reason to suspect that a glass ceiling exists.

[peterderivaz]

Interestingly, Wikipedia disagrees.

For a radix of 10, there is thought to be no number with a multiplicative persistence > 11: this is known to be true for numbers up to 10 to the power of 50.

http://en.wikipedia.org/wiki/Persistence_of_a_number

I guess the problem is that when you multiply lots of digits together you become increasingly likely to end up with a 0 digit somewhere.

[crondee]

Thanks for the link, I dug a little more and came across [1] which mentions a contribution by erdos to the effect that persistence might not be bounded. I guess I might spend some time to figure out number 12 :) [1] http://web.archive.org/web/20050214141815/http://www.wschnei...