July 2002
Intermediate to advanced
320 pages
8h 15m
English
Content preview from Hacker's Delight
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16-2. Willans’s Formulas
C. P. Willans gives the following formula for the nth prime [Will]:
The derivation starts from Wilson’s theorem, which states that p is prime or 1 if and only if (p − 1)! ≡ −1(mod p). Thus,
is an integer for x prime or x = 1 and is fractional for all composite x. Hence
Equation 1
Thus, if π(m) denotes [2] the number of primes ≤ m,
[2] Our apologies for the two uses of π in close proximity, but it’s standard notation and ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.