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Piprimes

From Rosetta Code
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



ALGOL 68[edit]

BEGIN # Show some values of pi(n) - the number of priems <= n  #
    # reurns a sieve of primes up to n #
    PROC prime sieve = ( INT n )[]BOOL:
         BEGIN
            [ 1 : n ]BOOL p;
            p[ 1 ] := FALSE; p[ 2 ] := TRUE;
            FOR i FROM 3 BY 2 TO n DO p[ i ] := TRUE  OD;
            FOR i FROM 4 BY 2 TO n DO p[ i ] := FALSE OD;
            FOR i FROM 3 BY 2 TO ENTIER sqrt( n ) DO
                IF p[ i ] THEN FOR s FROM i * i BY i + i TO n DO p[ s ] := FALSE OD FI
            OD;
            p
         END # prime sieve # ;
    # show pi(n) for n up to 21 #
    INT max number = 100; # guess of how large the primes we need are #
    INT max pi     = 21;
    []BOOL prime   = prime sieve( max number );
    INT pi        := 0;
    FOR i TO max number
    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

AWK[edit]

 
# 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[edit]

FreeBASIC[edit]

#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[edit]

    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

C[edit]

#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[edit]

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

F#[edit]

 
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions 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

Fermat[edit]

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[edit]

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

J[edit]

}[email protected](>:@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

Julia[edit]

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

PARI/GP[edit]

n=0; p=0
while(n<22, print(n); if(isprime(p),n=n+1);p=p+1)

Phix[edit]

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

Raku[edit]

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[edit]

/*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.     */
@pips= ' number of primes that are  (for all  N)  ≤  prime(22)   which is '   commas(@.hi)
if cols>0 then say ' index │'center(@pips,   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.*/
say
say 'Found '       commas(j-1)",  the"        @pips
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 [email protected].#+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[edit]

 
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...

Wren[edit]

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
    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.
Retrieved from "https://rosettacode.org/mw/index.php?title=Piprimes&oldid=330420"
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