This number is a prime.

+ 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 π/4 = 4 arctan(1/5) - arctan(1/239). Shanks used this to calculate π 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.

+ The smallest prime factor of the palindrome 1234567654321. Note that 239 is the smallest prime with period length 7 (the palindrome's middle digit). [Yates]

+ 2392 + 1 = 2 * 134. [Ljunggren]

+ A total cholesterol level of over 239 milligrams per deciliter is considered to be high.

+ The largest number that cannot be written as the sum of at most eight positive cubes: 239 = 5^3 + 3^3 + 3^3 + 3^3 + 2^3 + 2^3 + 2^3 + 2^3 + 1^3.

+ 239 requires nineteen fourth powers to represent it. [Deshouillers]

+ 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.

+ In a breeder reactor, uranium nuclei absorb neutrons to produce plutonium-239.

+ K. 239 (Serenata Notturna) is Mozart's only work for two orchestras. [Schroeppel]

+ HAKMEM, alternatively known as AI Memo 239, is a technical report of the MIT AI Lab that describes a wide variety of hacks, primarily useful and clever algorithms for mathematical computation.

+ 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]

+ In The Simpsons episode "Homer's Night Out," Homer weighs himself at 239 pounds and resolves to exercise.

+ Saint Petersburg Lyceum 239 is a public high school in Russia that specializes in mathematics and physics. Among its famous alumni is Yuri Matiyasevich, who solved Hilbert's tenth problem.

+ Arctan(1/239) in degrees begins 0.239..., and this is the only positive integer for which this is true. [Wu and Caldwell]

+ 239 is conjectured to be the largest number n such that n! can be written as the product of distinct factors in the range from n+1 to 2n, inclusive. [Chandler and Noe]

+ 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]

+ 239 is the 3rd NSW prime, following 7 and 41. Note that 7 + 41 + 239 = 7 * 41. [Menhinick]

+ The number of composite-numbered days of the month in both leap years and non-leap years. [Homewood]

+ The smallest prime in the only case of four 3-digit primes of forms, 4p+3, 6p+5, 8p+7, 10p+9, where p is a prime, (case p=59), i.e., 239, 359, 479, 599. Note that these forms have the general form kn+(k-1), where k is each of the first four even composite numbers, 4, 6, 8, 10. [Loungrides]

+ The first member of the smallest prime quadruple in 6p-1 progression: (239, 1433, 8597, 51581). [Bajpai]

+ The number of missing on board Malaysia Airlines Flight 370, which disappeared on 8 March 2014 while flying from Kuala Lumpur International Airport, Malaysia, to its destination, Beijing Capital International Airport in China.

+ The reversal of the 239th prime number (1499) is the 239th emirp (9941). [Gaydos]

+ The first known observation of Halley's Comet took place in 239 B.C., according to the European Space Agency.

+ The 52nd prime number (239) has a Collatz trajectory length of 52. [Gaydos]

+ The smallest integer greater than 1 that has the same Collatz trajectory length (52) as its square (57121). [Gaydos]

+ If A = 3, B = 5, C = 7, ... , Z = 137, using the regular prime alphabet, then 'PRIME' is a regular prime. [Homewood]

+ The twenty-second prime number of the form n!+239 is arguably most interesting! [Honaker]

+ The Collatz trajectory length of 239 equals π(239). Is there another odd prime with this property? [Sariyar]

+ Dr. Stephen Camarata studied 239 children in the United States during his research on Einstein Syndrome. [Foil]

+ There are 239 prime numbers p less than ten million for which the number of primes congruent to 1 (mod 4) up to p is greater than the number of primes congruent to 3 (mod 4) up to p. [Nie]

(There are 11 curios for this number that have not yet been approved by an editor.)

Printed from the PrimePages <t5k.org> © G. L. Honaker and Chris K. Caldwell