Has anyone invesitgated what is the fastest way to generate prime numbers sequentially in Mathematica, and whether this is effectively parallelizable? I’m trying to do some statistics on prime numbers and right now I am generating them in batches of size ‘chunk’, something like this: (* chunk is a…

Depends on the size. For 10 digits I would expect your method to be fine, although using NextPrime is faster. Each of the below were done from a clean start so as to remove cache effects. In[1]:= Timing[p1 = NextPrime[252097800623, Range[100]];] (* Out[1]= {0.004000, Null} *) In[1]:= Timing[p2 = …

Is it feasible to parallelize listing primes sequentially using Mathematica? Generally, Prime won’t compute all primes up to n. Prime[10^6] is much faster than Prime@Range[10^6]. If this weren’t true, then parallelization wouldn’t be feasible as all the work would be duplicated among subkernels. …

I do not recall whether or where NextPrime switches methods. As for parallelization, if you are in a range where Prime works then you might try a ParallelTable. Below is more or less what you did and it seems to give a notable speed boost in the range in question. p1 = Prime[10^10]; n = 10^5; firs…

Actually one can do quite well in regions above the working zone of Prime. Say we want to get the first n primes larger than m, and we intend to parallelize over nproc processors. We can get reasonable approximations of where the n/nproc groupings begin, overshoot each by some fraction, and take Uni…

Fastest way to generate prime numbers

Questions

samcarrettie (Sam Carrettie) April 1, 2014, 10:04pm 2

Pointing out a somewhat related discussion - perhaps there are some tidbits there:

How to find the first 100 prime twins without a do loop or iteration

I wonder if MSE has some related discussions - but have not found any yet.

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Find the "nth" of a large PrimeNumber? Questions mathematica , wolfram-alpha , discrete-mathematics	14	19002	August 13, 2018
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Fastest way to generate prime numbers

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