Definition
Plain language
A number from a particular famous sequence that grows explosively fast, named after a seventeenth-century mathematician.
As stated in the literature
Numbers of the form 2^(2^n)+1; whether every Fermat number is square-free is an open problem, and was among the unsolved conjectures the agents 'proved'.
Also called: Fermat numbers
Why it matters: Some basic questions about these numbers remain unanswered after centuries, which makes them a useful yardstick for testing whether a claimed mathematical breakthrough is real.
For example, the sequence starts 3, 5, 17, 257, 65537 — and the very next one is already over four billion.
Heard on the show
“And some were still open — conjectures no mathematician has proved, such as whether every Fermat number is square-free.”Episode 260 — One Line of Lean Faked 34 Proofs, and 99 Agents Copied It