This number is a prime.
There are 2339 ways to arrange the set of twelve pentominoes into a 6-by-10 rectangle, excluding trivial variations obtained by rotation and reflection of the whole rectangle, but including rotation and reflection of a subset of pentominoes. This case was first solved in 1960 by C. B. Haselgrove and Jenifer Haselgrove (now Jenifer Leech).
The smallest prime whose fourth power is pandigital (i.e., containing all digits from 0 to 9). [Gupta]
The sum of the first 2339 (a prime total) odd composites (9 + 15 + 21 + ... + 6321) is a palindromic prime (7576757). [De Geest]
(There is one curio for this number that has not yet been approved by an editor.)
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