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27th March 2017, 04:46 AM

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Posts: 6,555


Re: Programming Challenge  list prime numbers
Here's an example in Tcl for listing the first N >= 1 primes. For this you'll need the Tcllib package from the Fedora repos (dnf install tcllib).
Save this script as getPrimes.tcl:
Code:
#!/usr/bin/tclsh
package require math::numtheory
puts nonewline "2"
set N [lindex $argv 0]
set counter 1
set p 3
while {$counter < $N} {
if {[math::numtheory::isprime $p] == 1} {
puts nonewline ", $p"
incr counter
}
incr p 2
}
puts ""
Running the program to list the first 150 primes:
Code:
$ ./getPrimes.tcl 150
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647,
653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757,
761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863
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27th March 2017, 07:45 AM

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Re: Programming Challenge  list prime numbers
Here is my latest version. It removes the even numbers from the sieve, eliminates a lot of modulo operations, and multithreads the output. The downside is that you have to concatenate the output files, but there was nothing in the specifications saying the list had to be all in one file
Code:
// a multithreaded seive of Eratosthenes
//
#include <cstdio>
#include <cstdlib>
#include <vector>
#include <bitset>
#include <thread>
#include <cmath>
using namespace std;
typedef unsigned long int ul64;
//
// Use a bitset to hold the flags indicating if we
// have found a prime.
// The size should be small enough to fit in a CPU cache (32KB)
// given that the bitset stores 8 bits per byte.
// Each bit (at position i) represents if the number at 2*i+1 is a prime.
const ul64 BITSETSZ = 200000;
typedef bitset<BITSETSZ> Bits;
// Ideally this would be determined at run time.
const int NumThreads = 4;
// 
// mapping between integers and indexes
inline ul64 n2x( ul64 n ) { return (n1)/2; }
inline ul64 x2n( ul64 x ) { return x*2+1; }
// Provide our own alternative to printf that is dedicated to
// printing integers and buffers its results to reduce I/O overhead.
//
inline void print_int(ul64 val, FILE *fp)
{
// keep a buffer for each thread
thread_local char outbuf[4096];
thread_local int p = 0;
char chars[16];
int digits = 0;
//
// Pass zero to flush the buffer.
if ( val == 0 )
{
fwrite(outbuf, 1, p, fp );
p = 0;
return;
}
do
{
chars[digits++] = ((val % 10) + 0x30);
val /= 10;
} while (val && digits < 16);
while (digits>0)
{
outbuf[p++] = chars[digits];
}
outbuf[p++] = '\n';
if ( p > 4080 )
{
fwrite(outbuf, 1, p, fp );
p = 0;
}
}
// 
void print_page( Bits &p, ul64 pageNum, ul64 limit, FILE *fp )
{
bool firstPage = (pageNum == 0);
bool lastPage = ((pageNum+1)*BITSETSZ*2 >= limit);
if( firstPage && lastPage )
{
print_int(2, fp);
for( ul64 i=1, k; (k=x2n(i))<=limit; i++ )
{
if( p[i] ) print_int( k, fp );
}
}
else if( firstPage )
{
print_int(2, fp);
for(ul64 i=1; i<BITSETSZ; i++)
{
if( p[i] ) print_int( x2n(i), fp );
}
}
else if( lastPage )
{
ul64 x = pageNum * BITSETSZ;
for( ul64 i=0; x2n(x+i)<=limit; i++ )
{
if( p[i] ) print_int( x2n(x+i), fp );
}
}
else
{
ul64 x = pageNum * BITSETSZ;
for( ul64 i=0; i<BITSETSZ; i++ )
{
if( p[i] ) print_int( x2n(x+i), fp );
}
}
}
// 
void cull_pages( vector<Bits> & primes, ul64 limit, int thread, FILE *fp )
{
//
// cull out the multiples of each prime on each page
//
ul64 numPages = primes.size();
Bits & primeSetZero = primes[0];
//
// determine range of pages for this thread.
//
ul64 R = (numPages  1) / NumThreads;
ul64 startPage = (thread  1) * R + 1;
ul64 endPage = startPage + R;
if ( thread == NumThreads )
{
endPage = numPages;
}
//
// calculate the offsets for first page
//
vector<pair<ul64,ul64> > offsets; // first is prime, second is offset
for ( ul64 i=1; i<BITSETSZ; i++ )
{
ul64 P = startPage * (BITSETSZ * 2);
if ( primeSetZero[i] )
{
ul64 j = x2n(i);
ul64 k = P % j;
k = P  k + j;
if (!( k & 0x01) ) k += j;
k = n2x(kP);
offsets.push_back(make_pair(j,k));
}
}
//
// process the pages for this thread
//
for( ul64 p=startPage; p<endPage; p++ )
{
Bits & primeSet = primes[p];
for( auto &pr : offsets )
{
ul64 j = pr.first;
ul64 k = pr.second;
//
// cull out the multiples
//
while( k < BITSETSZ )
{
primeSet[k] = false;
k += j;
}
//
// update offset for next page
pr.second = k  BITSETSZ;
}
print_page( primeSet, p, limit, fp );
}
// flush the output buffer
print_int(0, fp);
}
// 
int main(int argc,char *argv[])
{
ul64 limit = atoll(argv[1]);
printf("Calculating primes up to: %lu\n",limit);
//
// make sure we include the end in our seive
limit++;
//
// The largest factor of limit is sqrt(limit)
ul64 range = sqrt( limit );
if ( BITSETSZ * 2 < range )
{
//
// Limit ourselves to 40 billion
ul64 n = ul64(4) * BITSETSZ * BITSETSZ;
printf( "max range for program is %lu\n", n );
return 1;
}
//
// Now we need enough bitsets to hold the entire range
// These are just the odd numbers
vector< Bits > primes( limit / BITSETSZ / 2 +1);
//
// initialise to set;
for( auto &b : primes) b.set();
//
// first we calc the primes for the first page
Bits & primeSetZero = primes[0];
ul64 rng = n2x(sqrt(x2n(BITSETSZ)));
for( ul64 i=1; i<=rng; i++)
{
if( primeSetZero[i] )
{
ul64 j = x2n(i);
ul64 k = n2x(j*j);
while( k < BITSETSZ )
{
primeSetZero[k] = false;
k += j;
}
}
}
FILE *f[NumThreads+1];
f[0] = fopen("primes70.dat", "w");
print_page( primeSetZero, 0, limit, f[0] );
print_int(0, f[0]);
//
// Then we cull the remaining pages.
// start the threads
std::thread threads[NumThreads];
for (int t=1; t<=NumThreads; t++ )
{
char fname[20];
sprintf(fname, "primes7%d.dat", t );
f[t] = fopen(fname, "w");
// std::ref is our promise that primes will hang around
// until the thread finishes.
threads[t1] = std::thread( cull_pages, std::ref(primes), limit, t, f[t] );
}
//
// Wait until they are done
for (int t=0; t<NumThreads; t++ )
{
threads[t].join();
}
//
// tidy up the files
//
for( int i=0; i<=NumThreads; i++ )
{
fclose(f[i]);
}
return 0;
}
It is quite quick:
Code:
[brenton@acer primes]$ time ./primes7 1000000000
Calculating primes up to: 1000000000
real 0m2.918s
user 0m8.508s
sys 0m0.981s
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That's very old fashioned thinking.
The current model is that it's holographic nested virtualities of turtles, all the way down.

27th March 2017, 04:46 PM

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Location: Montreal, Que, Canada
Posts: 4,008


Re: Programming Challenge  list prime numbers
I like APL. Here is a one line expression for the sieve of Eratosthenes based on variable X
For the fun of it I assigned X 199
Code:
(2=+⌿0=(⍳X)∘.⍳X)/⍳X←199
The Response
Code:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197
199
Here it is again for the primes under 100
Code:
(2=+⌿0=(⍳X)∘.⍳X)/⍳X←100
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
The logic is as follows.
"Build a matrix X by X , Eliminate all rows which are multiples of two above 2"
then scan the matrix (across the columns), eliminating rows where a modulo zero occurred.
and VOILA.
Last edited by lsatenstein; 29th March 2017 at 12:02 AM.

28th March 2017, 02:53 AM

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Join Date: Oct 2010
Location: Canberra
Posts: 2,531


Re: Programming Challenge  list prime numbers
Quote:
Originally Posted by lsatenstein
I like APL. Here is a one line expression for the of Eratosthenes based on variable X
Code:
(2=+⌿0=(⍳X)∘.⍳X)/⍳X←100
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
The logic is as follows.
"Build a matrix X by X , Eliminate all rows which are multiples of two above 2"
then scan the matrix (across the columns), eliminating rows where a modulo zero occurred.
and VOILA.

Very concise.
However, I suspect few of us know the APL symbols, so how it works is a bit too opaque for a thread that is aiming to illustrate various programming alternatives.
Secondly, you say that your solution uses an X by X matrix. Does this mean that it is O(N^2) in space and time requirements ?
__________________
Has anyone seriously considered that it might be turtles all the way down?
That's very old fashioned thinking.
The current model is that it's holographic nested virtualities of turtles, all the way down.

28th March 2017, 05:19 AM

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Join Date: Nov 2006
Location: Detroit
Posts: 6,555


Re: Programming Challenge  list prime numbers
Quote:
Originally Posted by ocratato
how it works is a bit too opaque for a thread that is aiming to illustrate various programming alternatives

Eh, I don't see a problem with being "too opaque." Part of the fun of these threads is trying to figure out how the heck people did what they did. To be honest, I'm not sure that lsatanstein's APL code is all that much more "opaque" than your latest 200+ line C++ program.
Your second objection, about scalability, is the more legitimate one. lsatanstein only ran it for prime numbers less than 100, so he got a 100 by 100 matrix. I'd like to see how his program runs with 1 million as the upper limit. I suspect it might have problems.
For example, I am somewhat familiar with APL, so I was able to translate his program into its equivalent in the J programming language, which is an APLish clone/imitator. For primes up to 100 it works fine:
Code:
$ jconsole
X =. 100
(2=(X$1) +/ . * 0=(1+i.X)/(1+i.X)) # (1+i.X)
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
But after a certain point it pretty much gives up:
Code:
X =. 1000
echo (2=(X$1) +/ . * 0=(1+i.X)/(1+i.X)) # (1+i.X)
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313
317 331 337 347 349 353 3...
That "3..." after 353 was put there by J. But it gets worse:
Code:
X =. 1000000
(2=(X$1) +/ . * 0=(1+i.X)/(1+i.X)) # (1+i.X)
out of memory
 (2=(X$1)+/ .*0=(1+i.X) /(1+i.X))#(1+i.X)
So yeah, I suspect lsatanstein's program might have similar issues.
I think from now on an upper limit of 1 million should be the minimum that an example in this thread should be able to do.
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28th March 2017, 03:10 PM

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Location: USA
Posts: 355


Re: Programming Challenge  list prime numbers
Quote:
Originally Posted by RupertPupkin
I think from now on an upper limit of 1 million should be the minimum that an example in this thread should be able to do.

This is why I am so dissatisfied with my original program and why I have been studying the submissions of others. I need to advance my Python and C skills and maybe pick up a few of these other languages  my original program chokes on a million, at least on my machine. Life is too short...
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28th March 2017, 08:54 PM

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Age: 28
Posts: 1,157


Re: Programming Challenge  list prime numbers
Quote:
Originally Posted by hiGuys
This is why I am so dissatisfied with my original program and why I have been studying the submissions of others. I need to advance my Python and C skills and maybe pick up a few of these other languages  my original program chokes on a million, at least on my machine. Life is too short...

I don't think knowing the specifics of the language is going to help you as much as knowing the cost of doing something. My first attempt at Eratosthenes Sieve in Python took a long time because I was deleting numbers in my list which isn't cheap. I think it's O(n) to do that per number. Just on one set of multiples that gets expensive fast. I then figured out that creating another list was less expensive than removing elements from an existing one. This is where learning about data structures and their performance helps.
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28th March 2017, 11:15 PM

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Age: 28
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Re: Programming Challenge  list prime numbers
Here is my Haskell solution.
Setting this up is going to involve a bit more work due to using Stack. Because of that I'm going to paste the source file here, but to build it you should look at the repo on GitHub. https://github.com/flounders/eratosthenes
I'm pretty pleased with the performance. At first I thought IO was aweful hence the TextShow imports, but the speed issues with the output were just tmux.
Code:
module Main where
import Control.Monad.ST
import Data.Vector (Vector, MVector)
import qualified Data.Vector as V
import Data.Vector.Mutable (STVector)
import qualified Data.Vector.Mutable as MV
import System.Environment (getArgs)
import TextShow
import TextShow.Data.Vector
main :: IO ()
main = do
args < getArgs
case args of
[] > putStrLn "No arguments given."
(x:_) > printT . sieve $ read x
sieve :: Int > Vector Int
sieve l = V.map fst . V.filter ((==) True . snd) $ V.zip v marked
where markIfPrime i vec
 i >= div (MV.length vec) 2 = return ()
 otherwise = do
x < MV.read vec i
if x
then do
let step = (v V.! i)
markOff vec (i+step) step
markIfPrime (i+1) vec
else markIfPrime (i+1) vec
v = V.iterateN (l1) (+1) 2
markOff vec i step
 i >= MV.length vec = return ()
 otherwise = do
MV.write vec i False
markOff vec (i+step) step
marked = runST $ do
mv < MV.replicate l True
markIfPrime 0 mv
V.freeze mv
Code:
stack exec eratosthenes 1000000 0.35s user 0.05s system 14% cpu 2.701 total
To build it install Haskell Stack according to the instructions here: https://docs.haskellstack.org/en/stable/README/
After that is done, in my repo run the following commands:
Code:
$ stack setup
$ stack build
$ stack exec eratosthenes 1000 # you can change 1000 to whatever number you want, but I wouldn't advise going past 10000000 if you want to see results in the first 10 minutes.
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29th March 2017, 12:12 AM

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Join Date: Jun 2005
Location: Montreal, Que, Canada
Posts: 4,008


Re: Programming Challenge  list prime numbers
Quote:
Originally Posted by RupertPupkin
Eh, I don't see a problem with being "too opaque." Part of the fun of these threads is trying to figure out how the heck people did what they did. To be honest, I'm not sure that lsatenstein's APL code is all that much more "opaque" than your latest 200+ line C++ program.
Your second objection, about scalability, is the more legitimate one. lsatenstein only ran it for prime numbers less than 100, so he got a 100 by 100 matrix. I'd like to see how his program runs with 1 million as the upper limit. I suspect it might have problems.
For example, I am somewhat familiar with APL, so I was able to translate his program into its equivalent in the J programming language, which is an APLish clone/imitator. For primes up to 100 it works fine:
Code:
$ jconsole
X =. 100
(2=(X$1) +/ . * 0=(1+i.X)/(1+i.X)) # (1+i.X)
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
But after a certain point it pretty much gives up:
Code:
X =. 1000
echo (2=(X$1) +/ . * 0=(1+i.X)/(1+i.X)) # (1+i.X)
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199
211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313
317 331 337 347 349 353 3...
That "3..." after 353 was put there by J. But it gets worse:
Code:
X =. 1000000
(2=(X$1) +/ . * 0=(1+i.X)/(1+i.X)) # (1+i.X)
out of memory
 (2=(X$1)+/ .*0=(1+i.X) /(1+i.X))#(1+i.X)
So yeah, I suspect lsatenstein's program might have similar issues.
I think from now on an upper limit of 1 million should be the minimum that an example in this thread should be able to do.

On a large number, my solution will die. There would be an n*2 sized matrix and an n sized vector.
J, is the successful effort to put APL code to plain text. The late Dr. Ken Iverson invented APL, and his son, moved that concept to J.
By the way, For the past 10 years I have been signing my postings with my first name. Isn't "Leslie" easier to remember? ( I corrected the spelling of my handle above)
I do like J, but I like APL even more.

29th March 2017, 12:53 AM

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Re: Programming Challenge  list prime numbers
Quote:
Originally Posted by hiGuys
Very impressive. I was going to install this mysterious Octave, but, at least on the machine I am currently in front of, it looks like a 237 MB installation with the necessary dependencies yet to be installed. Maybe in future...

Interesting on your proposed installation size.
Here is what I found:
Install 17 Packages
Total download size: 25 M
Installed size: 85 M
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29th March 2017, 04:55 AM

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Posts: 355


Re: Programming Challenge  list prime numbers
Quote:
Originally Posted by Flounder
I don't think knowing the specifics of the language is going to help you as much as knowing the cost of doing something. My first attempt at Eratosthenes Sieve in Python took a long time because I was deleting numbers in my list which isn't cheap. I think it's O(n) to do that per number. Just on one set of multiples that gets expensive fast. I then figured out that creating another list was less expensive than removing elements from an existing one. This is where learning about data structures and their performance helps.

I think it's fair at this point to say I don't even know what I don't know. But I will learn, with hard work and the help of kind souls along the way.
 Post added at 03:55 AM  Previous post was at 03:52 AM 
Quote:
Originally Posted by jims
Interesting on your proposed installation size.
Here is what I found:
Install 17 Packages
Total download size: 25 M
Installed size: 85 M

The particular machine I was working from is bare bones and a lot of the install was dependencies. This being a Fedora forum, I will probably give Octave a try on one of my Fedora installs next big break in time I get.
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29th March 2017, 06:39 AM

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Re: Programming Challenge  list prime numbers
No programming challenge would be complete without an example in Emacs Lisp. Disclaimer: Unlike my other examples, I didn't come up with this code myself  I found it on the interwebs.
Save this as getPrimes.el:
Code:
(defun sieve (limit)
(let ((xs (vconcat [0 0] (numbersequence 2 limit))))
(clloop for i from 2 to (sqrt limit)
when (aref xs i)
do (clloop for m from (* i i) to limit by i
do (aset xs m 0)))
(remove 0 xs)))
(print (sieve (stringtonumber (car argv))))
Then bytecompile it with Emacs:
Code:
$ emacs Q batch eval '(bytecompilefile "getPrimes.el")'
That will produce the file getPrimes.elc, which you can run like this:
Code:
$ emacs Q script getPrimes.elc <some_number>
The primes up to 1000:
Code:
$ emacs Q script getPrimes.elc 1000
[2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211
223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331
337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449
457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587
593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709
719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853
857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991
997]
Takes about 3 seconds to get the primes up to 1 million:
Code:
$ time emacs Q script getPrimes.elc 1000000 > primes.log
real 0m3.014s
user 0m2.919s
sys 0m0.057s
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30th March 2017, 05:24 AM

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Posts: 6,555


Re: Programming Challenge  list prime numbers
Here's another Octave example, this time using nothing more than some of Octave's convenient array indexing operations to produce somewhat of a vectorized approach. I think those array operations are a big part of what makes Octave/Matlab so powerful and even fun to use.
Save this as getPrimes2.m:
Code:
n = str2num(argv(){1});
nums = 1:n;
p = 2;
while p^2 <= n
nums(p^2:p:n) = 0;
p = find(nums > p, 1);
end
display(nums(nums > 1)')
Getting the primes less than 20:
Code:
$ octave qf getPrimes2.m 20
2
3
5
7
11
13
17
19
Takes just under 1.3 seconds to get the primes less than 1 million:
Code:
$ time octave qf getPrimes2.m 1000000 > primes.log
real 0m1.280s
user 0m1.196s
sys 0m0.069s
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7th April 2017, 04:06 AM

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Re: Programming Challenge  list prime numbers
Maxima, a computer algebra system available in the Fedora repos, has builtin support for this:
Code:
$ maxima veryquiet batchstring="primes(2,100);"
primes(2,100)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97]
Takes about 5.3 seconds to find the primes up to 1 million:
Code:
$ time maxima veryquiet batchstring="primes(2,1000000);" > primes.log
real 0m5.347s
user 0m4.994s
sys 0m0.245s
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