Is there a Limit to the Multiplicative Persistence of a Number?

Theorem

It has been conjectured that there may be an upper limit to the multiplicative persistence of a natural number.

Progress

It is not known whether there exists a number $n$ such that:

$\map P n = 12$

where $\map P n$ denotes the multiplicative persistence of $n$, but it is known that it is greater than $10^{200}$.

Sources

• 1973: N.J.A. Sloane: The persistence of a number (J. Recreational Math. Vol. 6: pp. 97 – 98)
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10$