10001th prime: Difference between revisions
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Automated syntax highlighting fixup (second round - minor fixes)
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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.
{{libheader|ALGOL 68-primes}}
<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?
print primes\[10000]</syntaxhighlight>
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=={{header|AWK}}==
<syntaxhighlight lang=
# syntax: GAWK -f 10001TH_PRIME.AWK
# converted from FreeBASIC
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=={{header|BASIC}}==
==={{header|BASIC256}}===
<syntaxhighlight lang=
if v < 2 then return False
if v mod 2 = 0 then return v = 2
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==={{header|PureBasic}}===
<syntaxhighlight lang=
If v <= 1 : ProcedureReturn #False
ElseIf v < 4 : ProcedureReturn #True
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==={{header|Yabasic}}===
<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>
#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 {
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
namespace p10001 // 1 second 10001 104743
{ class Program // rextester.com/ZBEPGE34760
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=={{header|C++}}==
{{libheader|Primesieve}}
<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#)]
<syntaxhighlight lang="fsharp">
// 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 ;
2 10,000 [ next-prime ] times .</syntaxhighlight>
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=={{header|Fermat}}==
<syntaxhighlight lang="fermat">
Prime(10001);
</syntaxhighlight>
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=={{header|FreeBASIC}}==
<syntaxhighlight lang="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>
{{out}}
<pre>
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=={{header|GW-BASIC}}==
<syntaxhighlight lang="gwbasic">10 PN=1
20 P = 3
30 WHILE PN < 10001
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=={{header|Go}}==
<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>
{{out}}
<pre>104743</pre>
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=={{header|Java}}==
Uses the PrimeGenerator class from [[Extensible prime generator#Java]].
<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
def primes: 2, (range(3; infinite; 2) | select(is_prime));
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=={{header|Julia}}==
<syntaxhighlight lang="julia">julia> using Primes
julia> prime(10001)
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</syntaxhighlight>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang=
{{out}}<pre>
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=={{header|PARI/GP}}==
<syntaxhighlight lang="parigp">prime(10001)</syntaxhighlight>
{{out}}<pre>%1 = 104743</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
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=={{header|Phix}}==
<!--<syntaxhighlight lang=
<span style="color: #008080;">with</span> <span style="color: #008080;">js</span> <span style="color: #0000FF;">?</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10001</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
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=={{header|Picat}}==
<syntaxhighlight lang=
println(nth_prime(10001)),
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=={{header|Python}}==
===Trial Division Method===
<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
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
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:
'Original version: 10001 104743 .21875
'This version: 10001 104743 .109375
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=={{header|R}}==
<syntaxhighlight lang=
nth_prime(10001)</syntaxhighlight>
{{out}}
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=={{header|Racket}}==
<syntaxhighlight lang=
(require math/number-theory)
; Index starts at 0, (nth-prime 0) is 2
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=={{header|Raku}}==
<syntaxhighlight lang=
{{out}}
<pre>104743</pre>
=={{header|REXX}}==
<syntaxhighlight lang="rexx">/* REXX */
Parse Version v
Say v
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=={{header|Ring}}==
<syntaxhighlight lang="ring">
load "stdlib.ring"
see "working..." + nl
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=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require "prime"
puts Prime.lazy.drop(10_000).next</syntaxhighlight>
{{out}}
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</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">// [dependencies]
// primal = "0.3"
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=={{header|Sidef}}==
<syntaxhighlight lang="ruby">say 10001.prime</syntaxhighlight>
{{out}}
<pre>
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{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascript">import "./math" for Int
import "./fmt" for Fmt
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=={{header|XPL0}}==
<syntaxhighlight lang=
int N, I;
[for I:= 3 to sqrt(N) do
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