10001th prime
- Task
Find and show on this page the 10001st prime number.
ALGOL 68
Chebyshev showed that the limit of pi( n ) / ( n / ln(n) ) as n approaches infinity is 1 ( pi( n ) is the number of primes up to n ).
The APPROXIMATESIEVESIZEFOR operator uses this to find a rough value for size of sieve needed to contain the required number of primes.
<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 #
INT required prime = 10 001;
[]BOOL prime = PRIMESIEVE APPROXIMATESIEVESIZEFOR required prime;
INT p count := 1;
FOR n FROM 3 BY 2 WHILE p count < required prime DO
IF prime[ n ] THEN
p count +:= 1;
IF p count = required prime THEN
print( ( "Prime ", whole( required prime, 0 ), " is ", whole( n, 0 ) ) )
FI
FI
OD
END</lang>
- Output:
Prime 10001 is 104743
AWK
<lang AWK>
- syntax: GAWK -f 10001TH_PRIME.AWK
- converted from FreeBASIC
BEGIN {
printf("%s\n",main(10001))
exit(0)
} function main(n, p,pn) {
if (n == 1) { return(2) }
p = 3
pn = 1
while (pn < n) {
if (is_prime(p)) {
pn++
}
p += 2
}
return(p-2)
} function is_prime(n, d) {
d = 5
if (n < 2) { return(0) }
if (n % 2 == 0) { return(n == 2) }
if (n % 3 == 0) { return(n == 3) }
while (d*d <= n) {
if (n % d == 0) { return(0) }
d += 2
if (n % d == 0) { return(0) }
d += 4
}
return(1)
} </lang>
- Output:
104743
C
<lang c>#include<stdio.h>
- include<stdlib.h>
int isprime( int p ) {
int i;
if(p==2) return 1;
if(!(p%2)) return 0;
for(i=3; i*i<=p; i+=2) {
if(!(p%i)) return 0;
}
return 1;
}
int prime( int n ) {
int p, pn=1;
if(n==1) return 2;
for(p=3;pn<n;p+=2) {
if(isprime(p)) pn++;
}
return p-2;
}
int main(void) {
printf( "%d\n", prime(10001) ); return 0;
}</lang>
- Output:
104743
C#
Comparing performance of the one-at-a-time 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, pr[10000] but since the array is zero based, it's the 10001st value.
<lang csharp>using System; class Program {
static bool isprime(uint p ) { if ((p & 1) == 0) return p == 2;
if ((p % 3) == 0) return p == 3;
for (uint i = 5, d = 4; i * i <= p; i += (d = 6 - d))
if (p % i == 0) return false; return true; }
static uint prime(uint n) { uint p, d, pn;
for (p = 5, d = 4, pn = 2; pn < n; p += (d = 6 - d))
if (isprime(p)) pn++; return p - d; }
static void Main(string[] args) {
Console.WriteLine("One-at-a-time vs sieve of Eratosthenes");
var sw = System.Diagnostics.Stopwatch.StartNew();
var t = prime(10001); sw.Stop(); double e1, e2;
Console.Write("{0:n0} {1} ms", prime(10001),
e1 = sw.Elapsed.TotalMilliseconds);
sw.Restart(); uint n = 105000, i, j; var pr = new uint[10100];
pr[0] = 2; pr[1] = 3; uint pc = 2, r, d, ii;
var pl = new bool[n + 1]; r = (uint)Math.Sqrt(n);
for (i = 9; i < n; i += 6) pl[i] = true;
for (i = 5, d = 4; i <= r; i += (d = 6 - d)) if (!pl[i]) {
pr[pc++] = i; for (j = i * i, ii = i << 1; j <= n; j += ii)
pl[j] = true; }
for ( ;i <= n; i += (d = 6 - d)) if (!pl[i]) pr[pc++] = i;
t = pr[10000]; sw.Stop();
Console.Write(" {0:n0} {1} μs {2:0.000} times faster", t,
(e2 = sw.Elapsed.TotalMilliseconds) * 1000.0, e1 / e2); } }</lang>
- Output @ Tio.run:
One-at-a-time vs sieve of Eratosthenes 104,743 3.8943 ms 104,743 357.9 μs 10.881 times faster
C++
<lang cpp>#include <iostream>
- include <locale>
- include <primesieve.hpp>
int main() {
std::cout.imbue(std::locale(""));
std::cout << "The 10,001st prime is " << primesieve::nth_prime(10001) << ".\n";
}</lang>
- Output:
The 10,001st prime is 104,743.
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // 10001st prime. Nigel Galloway: November 22nd., 2021 printfn $"%d{Seq.item 10000 (primes32())}" </lang>
- Output:
104743
Factor
<lang factor>USING: math math.primes prettyprint ;
2 10,000 [ next-prime ] times .</lang>
- Output:
104743
Fermat
<lang fermat> Prime(10001); </lang>
- Output:
104743
FreeBASIC
<lang freebasic>
- include "isprime.bas"
function prime( n as uinteger ) as ulongint
if n=1 then return 2
dim as integer p=3, pn=1
while pn<n
if isprime(p) then pn + = 1
p += 2
wend
return p-2
end function
print prime(10001) </lang>
- Output:
104743
GW-BASIC
<lang gwbasic>10 PN=1 20 P = 3 30 WHILE PN < 10001 40 GOSUB 100 50 IF Q = 1 THEN PN = PN + 1 60 P = P + 2 70 WEND 80 PRINT P-2 90 END 100 REM tests if a number is prime 110 Q=0 120 IF P = 2 THEN Q = 1: RETURN 130 IF P=3 THEN Q=1:RETURN 140 I=1 150 I=I+2 160 IF INT(P/I)*I = P THEN RETURN 170 IF I*I<=P THEN GOTO 150 180 Q = 1 190 RETURN</lang>
- Output:
104743
J
<lang j>p:10000 NB. the index starts at 0; p:0 = 2</lang>
- Output:
104743
Java
Uses the PrimeGenerator class from Extensible prime generator#Java. <lang java>public class NthPrime {
public static void main(String[] args) {
System.out.printf("The 10,001st prime is %,d.\n", nthPrime(10001));
}
private static int nthPrime(int n) {
assert n > 0;
PrimeGenerator primeGen = new PrimeGenerator(10000, 100000);
int prime = primeGen.nextPrime();
while (--n > 0)
prime = primeGen.nextPrime();
return prime;
}
}</lang>
- Output:
The 10,001st prime is 104,743.
jq
Works with gojq, the Go implementation of jq
A solution without any pre-determined numbers or guesses.
See Erdős-primes#jq for a suitable definition of `is_prime` as used here. <lang jq># Output: a stream of the primes def primes: 2, (range(3; infinite; 2) | select(is_prime));
- The task
- jq uses an index-origin of 1 and so:
nth(10000; primes)</lang>
- Output:
104743
Julia
<lang julia>julia> using Primes
julia> prime(10001) 104743 </lang>
Mathematica / Wolfram Language
<lang Mathematica>Prime[10001]</lang>
- Output:
104743
PARI/GP
<lang parigp>prime(10001)</lang>
- Output:
%1 = 104743
Perl
<lang perl>use strict; use warnings; use feature 'say';
- the lengthy wait increases the delight in finally seeing the answer
my($n,$c) = (1,0); while () {
$c++ if (1 x ++$n) !~ /^(11+)\1+$/; $c == 10_001 and say $n and last;
}
- or if for some reason you want the answer quickly
use ntheory 'nth_prime'; say nth_prime(10_001);</lang>
- Output:
104743 104743
Phix
with js ?get_prime(10001)
- Output:
104743
Raku
<lang perl6>say (^∞).grep( &is-prime )[10000]</lang>
- Output:
104743
REXX
<lang rexx>/* REXX */ Parse Version v Say v Call Time 'R' z=1 p.0=3 p.1=2 p.2=3 p.3=5 Do n=5 By 2 Until z=10001
If right(n,1)=5 Then Iterate Do i=2 To p.0 Until b**2>n b=p.i If n//b=0 Then Leave End If b**2>n Then Do z=p.0+1 p.z=n p.0=z End End
Say z n time('E')</lang>
- Output:
H:\>rexx prime10001 REXX-ooRexx_5.0.0(MT)_64-bit 6.05 8 Sep 2020 10001 104743 0.219000 H:\>regina prime10001 REXX-Regina_3.9.4(MT) 5.00 25 Oct 2021 10001 104743 .615000
Ring
<lang ring> load "stdlib.ring" see "working..." + nl num = 0 pr = 0 limit = 10001
while true
num++
if isprime(num) pr++ ok
if pr = limit exit ok
end
see "" + num + nl + "done..." + nl </lang>
- Output:
working... The 10001th prime is: 104743 done...
Ruby
<lang ruby>require "prime" puts Prime.lazy.drop(10_000).next</lang>
- Output:
104743
Rust
<lang rust>// [dependencies] // primal = "0.3"
fn main() {
let p = primal::StreamingSieve::nth_prime(10001);
println!("The 10001st prime is {}.", p);
}</lang>
- Output:
The 10001st prime is 104743.
Wren
<lang ecmascript>import "./math" for Int import "./fmt" for Fmt
var n = 10001 var limit = (n.log * n * 1.2).floor // should be enough var primes = Int.primeSieve(limit) Fmt.print("The $,r prime is $,d.", n, primes[n-1])</lang>
- Output:
The 10,001st prime is 104,743.
XPL0
<lang XPL0>func IsPrime(N); \Return 'true' if odd N > 2 is prime int N, I; [for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false; I:= I+1; ];
return true; ];
int C, N; [C:= 1; \count 2 as first prime N:= 3; loop [if IsPrime(N) then
[C:= C+1;
if C = 10001 then quit;
];
N:= N+2;
];
IntOut(0, N); ]</lang>
- Output:
104743