10001th prime: Difference between revisions

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The APPROXIMATESIEVESIZEFOR operator uses this to find a rough value for size of sieve needed to contain the required number of primes.

<syntaxhighlight lang=algol68>BEGIN # find the 10001st prime #

<syntaxhighlight lang="algol68">BEGIN # find the 10001st prime #

PR read "primes.incl.a68" PR

# construct a sieve of primes that should be large enough to contain 10001 primes #

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=={{header|Arturo}}==

<syntaxhighlight lang=rebol>primes: select 2..110000 => prime?

<syntaxhighlight lang="rebol">primes: select 2..110000 => prime?

print primes\[10000]</syntaxhighlight>

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=={{header|AWK}}==

# syntax: GAWK -f 10001TH_PRIME.AWK

# converted from FreeBASIC

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=={{header|BASIC}}==

==={{header|BASIC256}}===

<syntaxhighlight lang=~~BASIC256~~>function isPrime(v)

<syntaxhighlight lang="basic256">function isPrime(v)

if v < 2 then return False

if v mod 2 = 0 then return v = 2

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==={{header|PureBasic}}===

<syntaxhighlight lang=~~PureBasic~~>Procedure isPrime(v.i)

<syntaxhighlight lang="purebasic">Procedure isPrime(v.i)

If v <= 1 : ProcedureReturn #False

ElseIf v < 4 : ProcedureReturn #True

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==={{header|Yabasic}}===

<syntaxhighlight lang=yabasic>sub isPrime(v)

<syntaxhighlight lang="yabasic">sub isPrime(v)

if v < 2 then return False : fi

if mod(v, 2) = 0 then return v = 2 : fi

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=={{header|C}}==

<syntaxhighlight lang=c>#include<stdio.h>

<syntaxhighlight lang="c">#include<stdio.h>

#include<stdlib.h>

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===Sieve vs Trial Division===

Comparing performance of the one-at-a-time trial division method vs the sieve of Eratosthenes method. About ten times faster for the sieve. It may appear that the sieve may be off by one, <code>pr[10000]</code> but since the array is zero based, it's the 10001st value.

<syntaxhighlight lang=csharp>using System; class Program {

<syntaxhighlight lang="csharp">using System; class Program {

static bool isprime(uint p ) { if ((p & 1) == 0) return p == 2;

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===Alternative Trial Division Method===

<syntaxhighlight lang=csharp>using System; using System.Text; // PRIME_numb.cs russian DANILIN

<syntaxhighlight lang="csharp">using System; using System.Text; // PRIME_numb.cs russian DANILIN

namespace p10001 // 1 second 10001 104743

{ class Program // rextester.com/ZBEPGE34760

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=={{header|C++}}==

<syntaxhighlight lang=cpp>#include <iostream>

<syntaxhighlight lang="cpp">#include <iostream>

#include <locale>

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=={{header|F_Sharp|F#}}==

This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]

// 10001st prime. Nigel Galloway: November 22nd., 2021

printfn $"%d{Seq.item 10000 (primes32())}"

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</pre>

=={{header|Factor}}==

<syntaxhighlight lang=factor>USING: math math.primes prettyprint ;

<syntaxhighlight lang="factor">USING: math math.primes prettyprint ;

2 10,000 [ next-prime ] times .</syntaxhighlight>

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=={{header|Fermat}}==

Prime(10001);

</syntaxhighlight>

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=={{header|FreeBASIC}}==

#include "isprime.bas"

function prime( n as uinteger ) as ulongint

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=={{header|Frink}}==

<syntaxhighlight lang=frink>nth[primes[], 10001-1]</syntaxhighlight>

<syntaxhighlight lang="frink">nth[primes[], 10001-1]</syntaxhighlight>

<pre>

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=={{header|GW-BASIC}}==

<syntaxhighlight lang=gwbasic>10 PN=1

<syntaxhighlight lang="gwbasic">10 PN=1

20 P = 3

30 WHILE PN < 10001

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=={{header|Go}}==

<syntaxhighlight lang=go>package main

<syntaxhighlight lang="go">package main

import "fmt"

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=={{header|J}}==

<syntaxhighlight lang=j>p:10000 NB. the index starts at 0; p:0 = 2</syntaxhighlight>

<syntaxhighlight lang="j">p:10000 NB. the index starts at 0; p:0 = 2</syntaxhighlight>

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=={{header|Java}}==

Uses the PrimeGenerator class from [[Extensible prime generator#Java]].

<syntaxhighlight lang=java>public class NthPrime {

<syntaxhighlight lang="java">public class NthPrime {

public static void main(String[] args) {

System.out.printf("The 10,001st prime is %,d.\n", nthPrime(10001));

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See [[Erdős-primes#jq]] for a suitable definition of `is_prime` as used here.

<syntaxhighlight lang=jq># Output: a stream of the primes

<syntaxhighlight lang="jq"># Output: a stream of the primes

def primes: 2, (range(3; infinite; 2) | select(is_prime));

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=={{header|Julia}}==

<syntaxhighlight lang=julia>julia> using Primes

<syntaxhighlight lang="julia">julia> using Primes

julia> prime(10001)

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</syntaxhighlight>

=={{header|Mathematica}} / {{header|Wolfram Language}}==

<syntaxhighlight lang=~~Mathematica~~>Prime[10001]</syntaxhighlight>

<syntaxhighlight lang="mathematica">Prime[10001]</syntaxhighlight>

{{out}}<pre>

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=={{header|PARI/GP}}==

<syntaxhighlight lang=parigp>prime(10001)</syntaxhighlight>

<syntaxhighlight lang="parigp">prime(10001)</syntaxhighlight>

{{out}}<pre>%1 = 104743</pre>

=={{header|Perl}}==

<syntaxhighlight lang=perl>use strict;

<syntaxhighlight lang="perl">use strict;

use warnings;

use feature 'say';

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=={{header|Phix}}==

with js ?get_prime(10001)

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=={{header|Picat}}==

println(nth_prime(10001)),

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=={{header|Python}}==

===Trial Division Method===

<syntaxhighlight lang=python>#!/usr/bin/python

<syntaxhighlight lang="python">#!/usr/bin/python

def isPrime(n):

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===Alternative Trial Division Method===

<syntaxhighlight lang=python>import time; max=10001; n=1; p=1; # PRIME_numb.py russian DANILIN

<syntaxhighlight lang="python">import time; max=10001; n=1; p=1; # PRIME_numb.py russian DANILIN

while n<=max: # 78081 994271 45 seconds

f=0; j=2; s = int(p**0.5) # rextester.com/AAOHQ6342

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=={{header|QB64}}==

===Trial Division Method===

<syntaxhighlight lang=qbasic>max=10001: n=1: p=0: t=Timer ' PRIMES.bas russian DANILIN

<syntaxhighlight lang="qbasic">max=10001: n=1: p=0: t=Timer ' PRIMES.bas russian DANILIN

While n <= max ' 10001 104743 0.35 seconds

f=0: j=2

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===More Efficient TD Method===

<syntaxhighlight lang=qbasic>'JRace's results:

<syntaxhighlight lang="qbasic">'JRace's results:

'Original version: 10001 104743 .21875

'This version: 10001 104743 .109375

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=={{header|R}}==

<syntaxhighlight lang=R>library(primes)

<syntaxhighlight lang="r">library(primes)

nth_prime(10001)</syntaxhighlight>

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=={{header|Racket}}==

<syntaxhighlight lang=~~Racket~~>#lang racket

<syntaxhighlight lang="racket">#lang racket

(require math/number-theory)

; Index starts at 0, (nth-prime 0) is 2

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=={{header|Raku}}==

<syntaxhighlight lang=~~perl6~~>say (^∞).grep( &is-prime )[10000]</syntaxhighlight>

<syntaxhighlight lang="raku" line>say (^∞).grep( &is-prime )[10000]</syntaxhighlight>

=={{header|REXX}}==

<syntaxhighlight lang=rexx>/* REXX */

<syntaxhighlight lang="rexx">/* REXX */

Parse Version v

Say v

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=={{header|Ring}}==

load "stdlib.ring"

see "working..." + nl

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=={{header|Ruby}}==

<syntaxhighlight lang=ruby>require "prime"

<syntaxhighlight lang="ruby">require "prime"

puts Prime.lazy.drop(10_000).next</syntaxhighlight>

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</pre>

=={{header|Rust}}==

<syntaxhighlight lang=rust>// [dependencies]

<syntaxhighlight lang="rust">// [dependencies]

// primal = "0.3"

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=={{header|Sidef}}==

<syntaxhighlight lang=ruby>say 10001.prime</syntaxhighlight>

<syntaxhighlight lang="ruby">say 10001.prime</syntaxhighlight>

<pre>

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<syntaxhighlight lang=ecmascript>import "./math" for Int

<syntaxhighlight lang="ecmascript">import "./math" for Int

import "./fmt" for Fmt

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=={{header|XPL0}}==

<syntaxhighlight lang=~~XPL0~~>func IsPrime(N); \Return 'true' if odd N > 2 is prime

<syntaxhighlight lang="xpl0">func IsPrime(N); \Return 'true' if odd N > 2 is prime

int N, I;

[for I:= 3 to sqrt(N) do