- 239 (number)
239 (two hundred [and] thirty-nine) is the
natural number following 238 and preceding 240.In mathematics
It is a
prime number . The next is 241, with which it forms a pair oftwin prime s. 239 is aSophie Germain prime and aNewman-Shanks-Williams prime . It is anEisenstein prime with no imaginary part and real part of the form . Because the next odd number, 241 is prime, 239 is aChen prime .HAKMEM (incidentally AI memo 239 of theMIT AI Lab ) included an item on the properties of 239, including these:
* When expressing 239 as a sum ofsquare number s, 4 squares are required, which is the maximum that any integer can require; it also needs the maximum number (9) of positive cubes (23 is the only other such integer), and the maximum number (19) of fourth powers.
* 239/(13)2 is aconvergent to thecontinued fraction of thesquare root of 2 , so that 2392 = 2 · 134 - 1.
* Related to the above, π/4 = 4 arctan(1/5) - arctan(1/239).
* 239 · 4649 = 1111111, so 1/239 = 0.0041841 repeating, with period 7.
* 239 can be written as bn - bm - 1 for b = 2, 3, and 4, a fact evidenced by its binary representation 11101111, ternary representation 22212, and quaternary representation 3233.
* There are 239 primes < 1500.In other fields
239 is also:
* K239 is Mozart's only work for twoorchestra s.
* In "The Simpsons " episode "Homer's Night Out", Homer weighs himself and resolves to exercise. Six months later he weighs himself again and again resolves to exercise. Both times he weighed exactly 239 pounds. His weight was also seen in a daydream in the episodeKing-Size Homer
* The years A.D.239 and239 BC .
*239 is an area code representing part ofFlorida in theUnited States
*239 is a world famous lyceum of physics in mathematics inSaint-Petersburg ,Russia .
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