# Are All Triperfect Numbers Even?/Progress/Minimum Size

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## Theorem

It has been established that an odd triperfect number, if one were to exist, would be greater than $10^{70}$.

If it does not have $3$ as a prime factor, then it is greater than $10^{108}$.

## Proof

## Sources

- Jan. 1982: Walter E. Beck and Rudolph M. Najar:
*A Lower Bound for Odd Triperfects*(*Math. Comp.***Vol. 38**,*no. 157*: 249 – 251) www.jstor.org/stable/2007481

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $120$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $120$