Existence of Sociable Chain of Order 3

Open Question

Does there exist a sociable chain of order $3$?

Progress

No order $3$ sociable chain has been found less than $50 \, 000 \, 000$.

This article is complete as far as it goes, but it could do with expansion. In particular: The above statement comes from $1997$ -- there is a higher lower bound than this but I have not researched it. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. 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 {{Expand}} 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

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $12,496$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $12,496$