Piprimes
Piprimes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- Task
pi(n), the number of primes <= n, where pi(n) < 22
- Also see
-
- Prime-counting_function.
- Tables and hints by Tomás Oliveira e Silva.
- the OEIS entry: A0000720 pi(n), the number of primes <= n. Sometimes called PrimePi(n)....
11l
F is_prime(n)
I n == 2
R 1B
I n < 2 | n % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(n))).step(2)
I n % i == 0
R 0B
R 1B
V pi = 0
V n = 1
L
print(‘#2’.format(pi), end' I n % 10 == 0 {"\n"} E ‘ ’)
n++
I is_prime(n)
pi++
I pi == 22
L.break
print()- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Action!
INCLUDE "H6:SIEVE.ACT"
PROC Main()
DEFINE MAX="100"
BYTE ARRAY primes(MAX+1)
INT n=[0],p=[1]
Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
WHILE n<22
DO
PrintB(n) Put(32)
p==+1
IF primes(p) THEN
n==+1
FI
OD
RETURN- Output:
Screenshot from Atari 8-bit computer
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
ALGOL 68
BEGIN # Show some values of pi(n) - the number of priems <= n #
# show pi(n) for n up to 21 #
INT max prime = 100; # guess of how large the primes we need are #
INT max pi = 21;
PR read "primes.incl.a68" PR
[]BOOL prime = PRIMESIEVE max prime;
INT pi := 0;
FOR i TO UPB prime
WHILE IF prime[ i ] THEN pi +:= 1 FI;
pi <= max pi
DO
print( ( " ", whole( pi, -2 ) ) );
IF i MOD 10 = 0 THEN print( ( newline ) ) FI
OD
END- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Arturo
primes: select 2..1000 => prime?
piprimes: function [n] -> size select primes 'z [z =< n]
loop split.every: 10 select map 1..100 => piprimes => [& < 22] 'a ->
print map a => [pad to :string & 3]
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
AWK
# syntax: GAWK -f PIPRIMES.AWK
# converted from FreeBASIC
BEGIN {
while (1) {
if (is_prime(++curr)) {
running++
}
if (running == 22) {
break
}
printf("%3d%1s",running,++count%10?"":"\n")
}
printf("\nPiPrimes 1-%d: %d\n",running-1,count)
exit(0)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21 PiPrimes 1-21: 78
BASIC
BASIC256
function isPrime(v)
if v < 2 then return False
if v mod 2 = 0 then return v = 2
if v mod 3 = 0 then return v = 3
d = 5
while d * d <= v
if v mod d = 0 then return False else d += 2
end while
return True
end function
running = 0 : curr = 0 : limite = 22
while True
curr += 1
if isPrime(curr) then running += 1
if running = limite then exit while
print running; " ";
end while
end- Output:
Igual que la entrada de FreeBASIC.
FreeBASIC
#define UPTO 22
#include "isprime.bas"
dim as integer running = 0, curr=0
do
curr += 1
if isprime(curr) then running += 1
if running = UPTO then exit do
print running;" ";
loop
print : end- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Tiny BASIC
LET N = 0
LET P = 0
10 IF N = 22 THEN END
PRINT N
LET P = P + 1
GOSUB 100
20 IF Z = 1 THEN LET N = N + 1
GOTO 10
100 REM PRIMALITY BY TRIAL DIVISION
LET Z = 1
LET I = 2
110 IF (P/I)*I = P THEN LET Z = 0
IF Z = 0 THEN RETURN
LET I = I + 1
IF I*I <= P THEN GOTO 110
RETURNYabasic
sub isPrime(v)
if v < 2 then return False : fi
if mod(v, 2) = 0 then return v = 2 : fi
if mod(v, 3) = 0 then return v = 3 : fi
d = 5
while d * d <= v
if mod(v, d) = 0 then return False else d = d + 2 : fi
wend
return True
end sub
running = 0 : curr = 0 : limite = 22
do
curr = curr + 1
if isPrime(curr) then running = running + 1 : fi
if running = limite break
print running using "##", " ";
loop
end- Output:
Igual que la entrada de FreeBASIC.
C
#include <stdio.h>
#include <stdlib.h>
int isprime( int n ) {
int i;
if (n<2) return 0;
for(i=2; i*i<=n; i++) {
if (n % i == 0) {return 0;}
}
return 1;
}
int main(void) {
int n = 0, p = 1;
while (n<22) {
printf( "%d ", n );
p++;
if (isprime(p)) n+=1;
}
return 0;
}
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Cowgol
include "cowgol.coh";
sub isPrime(n: uint8): (r: uint8) is
var i: uint8 := 2;
r := 0;
if n>=2 then
while i*i <= n loop
if n%i == 0 then
return;
end if;
i := i + 1;
end loop;
r := 1;
end if;
end sub;
var count: uint8 := 0;
var n: uint8 := 1;
const MAX := 22;
while count < MAX loop
print_i8(count);
print_char('\t');
n := n + 1;
count := count + isPrime(n);
if n % 10 == 1 then
print_nl();
end if;
end loop;
print_nl();- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Dart
import 'dart:math';
import 'dart:io';
void main() {
int n = 0, p = 1;
while (n < 22) {
stdout.write("$n ");
++p;
if (isPrime(p)) ++n;
}
}
bool isPrime(int n) {
if (n <= 1) return false;
if (n == 2) return true;
for (int i = 2; i <= sqrt(n); ++i) {
if (n % i == 0) return false;
}
return true;
}
Delphi
function IsPrime(N: int64): boolean;
{Fast, optimised prime test}
var I,Stop: int64;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N+0.0));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
procedure ShowPiprimes(Memo: TMemo);
var N, P, Cnt: integer;
var S: string;
begin
N:= 0;
P:= 1;
Cnt:= 0;
S:='';
repeat
begin
S:=S+Format('%3D',[N]);
Inc(Cnt);
if (Cnt mod 10)=0 then S:=S+CRLF;
Inc(P);
if IsPrime(P) then N:= N+1;
end
until N >= 22;
Memo.Lines.Add(S);
end;
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21 Elapsed Time: 1.328 ms.
F#
This task uses Extensible Prime Generator (F#)
// PiPrimes: Nigel Galloway. April 5th., 2021
let fN=let i=primes32() in Seq.unfold(fun(n,g,l)->Some(l,if n=g then (n+1,Seq.head i,l+1) else (n+1,g,l)))(1,Seq.head i,0)
fN|>Seq.takeWhile((>)22)|>Seq.chunkBySize 20|>Seq.iter(fun n->Array.iter(printf "%2d ") n; printfn "")
- Output:
0 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Factor
USING: formatting grouping io lists math.primes
math.primes.lists math.ranges math.statistics sequences ;
21 lprimes lnth [1,b) [ prime? ] cum-count
10 group [ [ "%2d " printf ] each nl ] each
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Fermat
n:=0; p:=0
while n<22 do !n;!' ';p:=p+1;if Isprime(p)=1 then n:=n+1; fi; od- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
FOCAL
01.10 S C=0
01.20 S N=1
01.30 T %3,C
01.40 S N=N+1
01.50 D 2;S C=C+A
01.60 I (C-22)1.3
01.70 T !
01.80 Q
02.10 S I=1
02.20 S I=I+1
02.30 I (I*I-N-1)2.4;S A=1;R
02.40 S A=N/I
02.50 I (FITR(A)-A)2.2;S A=0- Output:
= 0= 1= 2= 2= 3= 3= 4= 4= 4= 4= 5= 5= 6= 6= 6= 6 = 7= 7= 8= 8= 8= 8= 9= 9= 9= 9= 9= 9= 10= 10= 11= 11 = 11= 11= 11= 11= 12= 12= 12= 12= 13= 13= 14= 14= 14= 14= 15= 15 = 15= 15= 15= 15= 16= 16= 16= 16= 16= 16= 17= 17= 18= 18= 18= 18 = 18= 18= 19= 19= 19= 19= 20= 20= 21= 21= 21= 21= 21= 21
FutureBasic
local fn IsPrime( n as NSUInteger ) as BOOL
BOOL isPrime = YES
NSUInteger i
if n < 2 then exit fn = NO
if n = 2 then exit fn = YES
if n mod 2 == 0 then exit fn = NO
for i = 3 to int(n^.5) step 2
if n mod i == 0 then exit fn = NO
next
end fn = isPrime
local fn Piprimes( limit as NSUInteger )
NSUInteger n = 0, p = 1
printf @"Piprimes from 1 through %lu:\n", limit
while ( n < limit )
printf @"%2lu \b", n
if p mod 10 == 0 then print
p++
if ( fn IsPrime(p) ) then n++
wend
end fn
fn Piprimes( 22 )
HandleEvents- Output:
Piprimes from 1 through 22: 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
J
}.@(>:@i.&.p:) 21
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Go
package main
import (
"fmt"
"rcu"
)
func main() {
primes := rcu.Primes(79) // go up to the 22nd
ix := 0
n := 1
count := 0
var pi []int
for {
if primes[ix] <= n {
count++
if count == 22 {
break
}
ix++
}
n++
pi = append(pi, count)
}
fmt.Println("pi(n), the number of primes <= n, where n >= 1 and pi(n) < 22:")
for i, n := range pi {
fmt.Printf("%2d ", n)
if (i+1)%10 == 0 {
fmt.Println()
}
}
fmt.Printf("\n\nHighest n for this range = %d.\n", len(pi))
}
- Output:
pi(n), the number of primes <= n, where n >= 1 and pi(n) < 22: 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21 Highest n for this range = 78.
jq
Works with gojq, the Go implementation of jq
This entry uses an approach based on streams of unbounded length; this has the advantage that no guessing or smarts is needed, either to provide a solution for the given bound (pi(n)<22) or any such bound.
For a suitable implementation of `is_prime` see e.g. Erdős-primes#jq.
Preliminaries
def count(s): reduce s as $x (null; .+1);
def emit_until(cond; stream):
label $out | stream | if cond then break $out else . end;
def next_prime:
if . == 2 then 3
else first(range(.+2; infinite; 2) | select(is_prime))
end;The task
# Generate pi($n) for $n > 0
def pi_primes:
foreach range(1; infinite) as $i ({n:0, np: 2}; # n counts, np is the next prime
if $i < .np then .
elif $i == .np then .n += 1 | .np |= next_prime
else .
end;
.n);
emit_until(. >= 22; pi_primes)- Output:
0 1 2 2 3 3 4 4 4 4 ... 19 19 19 19 20 20 21 21 21 21 21 21
Julia
using Primes
function listpiprimes(maxpi)
pmask = primesmask(1, maxpi * maxpi)
n = 0
for (i, isp) in enumerate(pmask)
isp == 1 && (n += 1) >= maxpi && break
print(rpad(n, 3), i % 10 == 0 ? "\n" : "")
end
end
listpiprimes(22)
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Mathematica/Wolfram Language
pi = PrimePi /@ Range[Prime[22] - 1];
Multicolumn[pi, {Automatic, 10}, Appearance -> "Horizontal"]
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Nim
import strutils
func isPrime(n: Natural): bool =
if n < 2: return false
if n mod 2 == 0: return n == 2
if n mod 3 == 0: return n == 3
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, 2
if n mod d == 0: return false
inc d, 4
result = true
var pi = 0
var n = 1
while true:
stdout.write ($pi).align(2), if n mod 10 == 0: '\n' else: ' '
inc n
if n.isPrime:
inc pi
if pi == 22: break
echo()
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
PARI/GP
n = 1;
while( primepi( n ) < 22,
printf( "%3d", primepi(n) );
if( n++ % 10 == 1,
print()) )- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Perl
use strict;
use warnings;
use feature 'state';
use ntheory 'is_prime';
my @pi = map { state $pi = 0; $pi += is_prime $_ ? 1 : 0 } 1..1e4;
do { print shift(@pi) . ' ' } until $pi[0] >= 22;
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Phix
with javascript_semantics integer ix = 1, n = 1, count = 0 sequence pi = {} while true do if get_prime(ix)<=n then count += 1 if count>=22 then exit end if ix += 1 end if n += 1 pi = append(pi,sprintf("%2d",count)) end while printf(1,"pi[1..%d]:\n%s\n",{length(pi),join_by(pi,1,10)})
- Output:
pi[1..78]: 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Quackery
isprime is defined at Primality by trial division#Quackery.
[ 0 swap
1 - times
[ i 1+ isprime + ] ] is pi ( n --> n )
2 [ dup pi dup 22 < while
echo sp 1+ again ]
2drop- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Raku
my @pi = (1..*).map: { state $pi = 0; $pi += .is-prime };
say @pi[^(@pi.first: * >= 22, :k)].batch(10)».fmt('%2d').join: "\n";
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
REXX
/*REXX program finds and displays pi(n) for 0 < N ≤ prime(22) {the 22nd prime is 87},*/
/*────────────────────────── where the pi function returns the number of primes ≤ N.*/
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 22 /* " " " " " " */
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
call genP /*build array of semaphores for primes.*/
w= 10 /*width of a number in any column. */
title= ' number of primes that are (for all N) ≤ prime(22) which is ' commas(@.hi)
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
idx= 1 /*initialize the index of output lines.*/
$=; pips= 0 /*a list of piPrimes numbers (so far). */
do j=1 for @.hi-1 /*gen list of piPrime numbers<prime(hi)*/
if !.j then pips= pips + 1 /*Is J prime? Then bump pips number.*/
if cols<0 then iterate /*Build the list (to be shown later)? */
c= commas(pips) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add a Frobenius #──►list, allow big #*/
if j//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'Found ' commas(j-1)", the" title /*display the foot separator for output*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: !.= 0 /*placeholders for primes (semaphores).*/
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */
#=5; s.#= @.# **2 /*number of primes so far; prime². */
/* [↓] generate more primes ≤ high.*/
do j=@.#+2 by 2 until #>hi /*find odd primes from here on. */
parse var j '' -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
/* [↑] the above 3 lines saves time.*/
do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return
- output when using the default inputs:
index │ number of primes that are (for all N) ≤ prime(22) which is 79 ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 0 1 2 2 3 3 4 4 4 4 11 │ 5 5 6 6 6 6 7 7 8 8 21 │ 8 8 9 9 9 9 9 9 10 10 31 │ 11 11 11 11 11 11 12 12 12 12 41 │ 13 13 14 14 14 14 15 15 15 15 51 │ 15 15 16 16 16 16 16 16 17 17 61 │ 18 18 18 18 18 18 19 19 19 19 71 │ 20 20 21 21 21 21 21 21 ───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── Found 78, the number of primes that are (for all N) ≤ prime(22) which is 79
Ring
load "stdlib.ring"
decimals(0)
see "working..." + nl
see "Piprimes are:" + nl
row = 0
limit1 = 400
Prim = []
for n = 1 to limit1
if isprime(n)
add(Prim,n)
ok
next
for n = 1 to len(Prim)
for m = 1 to len(Prim)
if Prim[m] > n
ind = m - 1
exit
ok
next
row = row + 1
see "" + ind + " "
if row%10 = 0
see nl
ok
next
see nl + "Found " + row + " Piprimes." + nl
see "done..." + nl- Output:
working... Piprimes are: 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21 Found 78 Piprimes. done...
Pi primes ✔
RPL
≪ 0 1 ROT FOR j j ISPRIME? + NEXT ≫ 'PI' STO ≪ 0 → n ≪ { } 1 CF DO 'n' INCR PI IF DUP 22 ≤ THEN + ELSE DROP 1 SF END UNTIL 1 FS? END ≫ 'TASK' STO
- Output:
1: { 0. 1. 2. 2. 3. 3. 4. 4. 4. 4. 5. 5. 6. 6. 6. 6. 7. 7. 8. 8. 8. 8. 9. 9. 9. 9. 9. 9. 10. 10. 11. 11. 11. 11. 11. 11. 12. 12. 12. 12. 13. 13. 14. 14. 14. 14. 15. 15. 15. 15. 15. 15. 16. 16. 16. 16. 16. 16. 17. 17. 18. 18. 18. 18. 18. 18. 19. 19. 19. 19. 20. 20. 21. 21. 21. 21. 21. 21. }
Ruby
require 'prime'
pi = 0
pies = (1..).lazy.map {|n| n.prime? ? pi += 1 : pi}.take_while{ pi < 22 }
pies.each_slice(10){|s| puts "%3d"*s.size % s}
- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
Sidef
1..(prime(22)-1) -> map { .prime_count }.say
- Output:
[0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 21]
Wren
import "/math" for Int
import "/seq" for Lst
import "/fmt" for Fmt
var primes = Int.primeSieve(79) // go up to the 22nd
var ix = 0
var n = 1
var count = 0
var pi = []
while (true) {
if (primes[ix] <= n) {
count = count + 1
if (count == 22) break
ix = ix + 1
}
n = n + 1
pi.add(count)
}
System.print("pi(n), the number of primes <= n, where n >= 1 and pi(n) < 22:")
for (chunk in Lst.chunks(pi, 10)) Fmt.print("$2d", chunk)
System.print("\nHighest n for this range = %(pi.count).")- Output:
pi(n), the number of primes <= n, where n >= 1 and pi(n) < 22: 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21 Highest n for this range = 78.
XPL0
func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true;
];
int Count, N, P;
[Count:= 0; N:= 0; P:= 1;
repeat if N<10 then ChOut(0, ^ );
IntOut(0, N);
Count:= Count+1;
if rem(Count/20) then ChOut(0, ^ ) else CrLf(0);
P:= P+1;
if IsPrime(P) then N:= N+1;
until N >= 22;
]- Output:
0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12 13 13 14 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 18 18 18 18 19 19 19 19 20 20 21 21 21 21 21 21
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