Are All Triperfect Numbers Even?/Progress/Minimum Size

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

This theorem requires a proof. In particular: Details You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• Jan. 1982: Walter E. Beck and Rudolph M. Najar: A Lower Bound for Odd Triperfects (Math. Comp. Vol. 38, no. 157: pp. 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): $120$