Den tor. 11. jul. 2019 kl. 15.40 skrev Bob Heffernan <
bob.heffer...@gmail.com>:
> On 19-07-11 09:31, James Geddes wrote:
> > Indeed, I would have thought that the calculation time would be
> > entirely dominated by the test for primality, and especially what
> > happens once the candidate primes are bigger than 2^64 and can no
> > longer be represented by a single word.
>
> I assume that you are right. The isprime procedure in my python code is
> the one from sympy (I didn't bother to include the import line in my
> previous email).
I believe that sympy uses the C library GMP.
> The prime? procedure in my Racket code is that from
> the math/number-theory library.
>
> I don't know anything about sympy, but I seem to recall that Python
> libraries for these sorts of things often rely on fast routines written
> in C. I suppose it might be interesting to implement the same
> prime-checking in both Python and Racket and *then* compare speeds.
>
If you want, you can use the prime test from GMP from Racket too.
#lang racket
(require gmp)
(define repetitions 25) ; manual says values between 15 and 50 are
reasonable.
(define (is-prime? n)
(case (mpz_probab_prime_p (mpz n) repetitions)
[(2) #t]
[(1) 'probably]
[(0) #f]))
(for/list ([n (in-range 2 100)]
#:when (is-prime? n))
n)
See https://docs.racket-lang.org/gmp/index.html?q=gmp and
https://gmplib.org/manual/Number-Theoretic-Functions.html
for more information.
/Jens Axel
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