Is there a Limit to the Multiplicative Persistence of a Number?
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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): $10$