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 >
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