What is this?

We're looking for a specific kind of number called square-cube pandigitals, or "nice numbers". A number is "nice" if the digits in its square and cube contain all possible values with no repeats. Right now the only known nice number is 69 (evaluated in base 10), but the math says if we expand our search to other bases there should be more, possibly infinitely many more! This site is a summary of our progress so far.

How can I help?

There are two main ways to help with this project.

The first is to lend your computational power, like with the old distributed computing initiatives such as SETI@Home. This repository has a program that connects to a central server and "checks out" a range to search for nice numbers. If you let it run it will report back with any results and credit those discoveries to your name!

The second is to help with the math. This site collects a lot of information from the clients, such as a log of highly-nice numbers and the "niceness" distribution for each range that you can query for analysis. You can use that data to find patterns or just attack the problem with pure theory at one of the discussion links below.

Where can I learn more?

• Jacob Cohen's excellent post over at Chromatic Conflux that started this whole thing. All of the original ideas and concepts are 100% from his efforts.
• Jacob's followup post on advances in the theory and procedure of finding nice numbers, including information on residue class filtering.
• The most recent prediction market on whether a nice number will be discovered by the end of March 2023 (it wasn't).
• The original prediction market that has since been closed but contains a lot of early advancements on the topic.