The largest prime factor of n2 + 1 is at least 17, provided n is greater than the prime number 239.
In 1706, Machin discovered that /4 = 4 arctan(1/5) - arctan(1/239). Shanks used this to calculate to 707 places in 1873, but only the first 527 digits were correct.
A solution to x4 + 1044 = 581362 + 1. [McLean]
Magic Square Lexicon: Illustrated by H. D. Heinz and J. R. Hendricks, includes 239 terms associated with magic squares, cubes, tesseracts, stars, etc.
2392 + 1 = 2 * 134. [Ljunggren]
239 requires nineteen fourth powers to represent it. [Deshouillers]
There are 21 primes of the form n! + 239. [Honaker]
The book Pandolfini's Endgame Course: Basic Endgame Concepts Explained by America's Leading Chess Teacher consists of 239 specific endgame positions, progressing from elementary endings to some subtle minor piece and pawn situations.
K. 239 (Serenata Notturna) is Mozart's only work for two orchestras. [Schroeppel]
Boland wrote 239#*2^239-1 is prime. Luhn found that 239#*2^239+/-1 are twins. [Luhn]
Professor Dick Solomon, lead character on the TV show Third Rock from the Sun, teaches his classes in room number 239. [Rupinski]
One saros cycle is almost exactly 239 anomalistic months. [McCranie]
Only two positive integers may not be written as the sum of nine non-negative cubes: 23 and 239. [Dickson]
239 = 2*3*5*11 - 7*13, proof of primality. [Wood]
1+3+5+7+....+237+239 = 239+241+243+...+335+337. Note that 239 and 337 are both primes. [Meller]
(There is one curio for this number that has not yet been approved by an editor.)
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