I clicked the link, and the result shows 78498 which jives with nth-prime On Tue, Dec 11, 2012 at 8:31 AM, Phil Bewig <pbe...@gmail.com> wrote:
> There must be an error in the prime-counting function. According to <a > href=" > http://www.wolframalpha.com/input/?i=how+many+primes+less+than+a+million";>Wolfram|Alpha</a>, > there are 79486 primes less than a million, not 78497. > > I don't use Racket, but I do have lots of Scheme code that computes with > prime numbers at my <a href="http://programmingpraxis.com>blog</a> that > you may find useful. > > On Tue, Dec 11, 2012 at 10:11 AM, Stephen Bloch <sbl...@adelphi.edu>wrote: > >> >> On Dec 11, 2012, at 9:03 AM, Jens Axel Søgaard wrote: >> >> > 2012/12/11 Stephen Bloch <bl...@adelphi.edu>: >> > >> >> Would it perhaps make more sense for small-primes to contain primes >> >> themselves, in increasing order so one can be found by binary search, >> rather >> >> than booleans? The O(1) behavior would be replaced by O(log(limit)), >> but >> >> perhaps you would save enough memory to put the limit higher. >> > >> > I think there are too many primes. >> > >> > Since >> > >> >> (require math) >> >> (nth-prime 78498) >> > 1000003 >> > >> > there are 78497 primes below a million. On a 64 bit machine >> > that requires 8*78497 = 627976 bytes. >> >> If you treated it as a vector whose elements were (compile-time-typed) >> 32-bit ints, that would cut it by a factor of 2, but it would still be a >> third of a megabyte. OTOH, a vector of bit-packed booleans would take an >> eighth of a megabyte for the same limit, and give you faster lookups. So >> you're right; my suggestion is probably not a win. >> >> How many primes are below ten million? A hundred million? At some point >> storing the primes will take less memory than storing primality flags, but >> that point may be above the size of tables we can realistically store today. >> >> Wait: it's conceivable that there is no such crossing point. As the >> numbers get big, it takes O(log(limit)) bits to store numbers less than >> limit. The number of primes less than limit is Theta(limit/log(limit)), so >> storing them all takes Theta(limit) space, asymptotically the same as >> storing the flags. >> >> >> >> >> Stephen Bloch >> sbl...@adelphi.edu >> >> >> ____________________ >> Racket Users list: >> http://lists.racket-lang.org/users >> > > > ____________________ > Racket Users list: > http://lists.racket-lang.org/users > >
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