# 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.

pi(n), the number of primes <= n, where pi(n) < 22

Also see

## 11l

Translation of: Nim
```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:
```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;
[]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

Translation of: FreeBASIC
```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
RETURN```

### Yabasic

Translation of: FreeBASIC
```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

Translation of: C
```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

Works with: Delphi version 6.0

```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;
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

Works with: Factor version 0.99 2021-02-05
```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

Translation of: Wren
Library: Go-rcu
```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: 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;```

```# 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)
n = 0
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

Library: ntheory
```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)
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

Works with: HP version 49g
```≪ 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
```
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

Library: Wren-math
Library: Wren-seq
Library: Wren-fmt
```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
}
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
```