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Two Hundred Thirty Nine
The MIT Artificial Intelligence
Laboratory Memo 239 (entitled HAKMEM) of February 1972 listed various properties
of the integer
239, some more interesting than others, such as: that 239 needs the maximum number
of powers in Waring's problem
for squares, cubes
and fourth powers; that it appears in Machin's formula for 
:
, the fraction
is a convergent
for the continued fraction
of 
; that since
(with 
being the prime counting function; etc. At the time, the memo couldn't have mentioned that 239 pounds is Homer Simpson's weight
(as established by at least two episodes of The Simpsons).
The prime
239, like many in its vicinity, is a Chen prime. As a Sophie Germain prime, it begins a Cunningham chain
of just length
2 (which ends with 479). On the plane
of Eisenstein integers, 239 is an Eisenstein prime
(its real part
being of the form 
and it not having an imaginary part), and it is also a Gaussian prime
(its real part being of the form 
); these two properties it has in common with all real primes
. Much more rare is that it is the third Newman-Shanks-Williams prime (the ninth is more than 
).