Find squares n where n+1 is prime: Difference between revisions
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Find squares '''n''' where '''n+1''' is prime and '''n<1.000'''
=={{header|ALGOL 68}}==
{{libheader|ALGOL 68-primes}}
<syntaxhighlight lang="algol68">BEGIN # find squares n where n + 1 is prime #
PR read "primes.incl.a68" PR
[]BOOL prime = PRIMESIEVE 1 000; # construct a sieve of primes up to 1000 #
# find the squares 1 less than a prime (ignoring squares of non-integers) #
# other than 1, the numbers must be even #
IF prime[ 2 # i.e.: ( 1 * 1 ) + 1 # ] THEN print( ( " 1" ) ) FI;
FOR i FROM 2 BY 2 TO UPB prime WHILE INT i2 = i * i;
i2 < UPB prime
DO
IF prime[ i2 + 1 ] THEN
print( ( " ", whole( i2, 0 ) ) )
FI
OD
END</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|ALGOL W}}==
Using the difference of two squares to optimise the primality tests and the square loop (similar to the Phix and Applescript samples), though with the small number of values to test, that probably doesn't affect runtime much...
<syntaxhighlight lang="algolw">
begin % find squares n where n + 1 is prime %
% returns true if n is prime, false otherwise, uses trial division %
logical procedure isPrime ( integer value n ) ;
if n < 3 then n = 2
else if n rem 3 = 0 then n = 3
else if not odd( n ) then false
else begin
logical prime;
integer f, f2, toNext;
prime := true;
f := 5;
f2 := 25;
toNext := 24; % note: ( 2n + 1 )^2 - ( 2n - 1 )^2 = 8n %
while f2 <= n and prime do begin
prime := n rem f not = 0;
f := f + 2;
f2 := toNext;
toNext := toNext + 8
end while_f2_le_n_and_prime ;
prime
end isPrime ;
% other than 1, the numbers must be even %
if isPrime( 2 % i.e.: ( 1 * 1 ) + 1 % ) then write( ( " 1" ) );
begin
integer i2, toNext;
toNext := i2 := 4; % note: ( 2n + 2 )^2 - 2n^2 = 8n + 4 %
while i2 < 1000 do begin
if isPrime( i2 + 1 ) then writeon( i_w := 1, s_w := 0, " ", i2 );
toNext := toNext + 8;
i2 := i2 + toNext
end while_i2_lt_1000
end
end.
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|AppleScript}}==
<syntaxhighlight lang="applescript">on isPrime(n)
if (n < 4) then return (n > 1)
if ((n mod 2 is 0) or (n mod 3 is 0)) then return false
repeat with i from 5 to (n ^ 0.5) div 1 by 6
if ((n mod i is 0) or (n mod (i + 2) is 0)) then return false
end repeat
return true
end isPrime
on task()
set output to {}
if (isPrime(1 * 1 + 1)) then set end of output to 1 * 1
repeat with sqrt from 2 to (1000 ^ 0.5) by 2
set n to sqrt * sqrt
if (isPrime(n + 1)) then set end of output to n
end repeat
return output
end task
task()</syntaxhighlight>
{{output}}
<syntaxhighlight lang="applescript">{1, 4, 16, 36, 100, 196, 256, 400, 576, 676}</syntaxhighlight>
{{trans|Phix}}
The first Phix solution's method of incrementing the square is fun, but not more efficient in AppleScript than the more straightforward method above. It can be optimised slightly by incrementing the ''d'' variable by 8 instead of incrementing by 4 and multiplying the result by 2. Also by incrementing the square + 1 each time instead of the square itself, so that 1 only has to be subtracted from the hits instead of being added to every square.
<syntaxhighlight lang="applescript">on task()
set output to {1}
set nPlus1 to 5
repeat with d from 12 to (1000 ^ 0.5 div 0.25) by 8
if (isPrime(nPlus1)) then set end of output to nPlus1 - 1
set nPlus1 to nPlus1 + d
end repeat
return output
end task</syntaxhighlight>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">1..31 | select 'x -> prime? 1 + x^2
| map 'x -> x^2
| print</syntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
=={{header|AutoHotkey}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="autohotkey">n := 0
while ((n2 := (n+=2)**2) < 1000)
if isPrime(n2+1)
result .= (result ? ", ":"" ) n2
MsgBox % result := 1 ", " result
return
isPrime(n, i:=2){
while (i < Sqrt(n)+1)
if !Mod(n, i++)
return False
return True
}</syntaxhighlight>
{{out}}
<pre>1, 4, 16, 36, 100, 196, 256, 400, 576, 676</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f FIND_SQUARES_N_WHERE_N+1_IS_PRIME.AWK
BEGIN {
start = 1
stop = 999
n = 2
n2 = n^2
printf("1")
count++
while (n2 < stop) {
if (is_prime(n2+1)) {
printf(" %d",n2)
count++
}
n += 2
n2 = n^2
}
printf("\nFind squares %d-%d: %d\n",start,stop,count)
exit(0)
}
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)
}
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
Find squares 1-999: 10
</pre>
=={{header|BASIC}}==
<syntaxhighlight lang="basic">10 DEFINT A-Z: N=1000
20 DIM C(N)
30 FOR P=2 TO SQR(N)
40 IF NOT C(P) THEN FOR C=P*P TO N STEP P: C(C)=1=1: NEXT
50 NEXT
60 FOR I=2 TO N
70 IF C(I) THEN 100
80 X=I-1: R=SQR(X)
90 IF R*R=X THEN PRINT X;
100 NEXT</syntaxhighlight>
{{out}}
<pre> 1 4 16 36 100 196 256 400 576 676</pre>
=={{header|BCPL}}==
<syntaxhighlight lang="bcpl">get "libhdr"
manifest $( MAX = 1000 $)
let isqrt(s) = valof
$( let x0 = s>>1 and x1 = ?
if x0 = 0 resultis s
x1 := (x0 + s/x0)>>1
while x1<x0
$( x0 := x1
x1 := (x0 + s/x0)>>1
$)
resultis x0
$)
let sieve(prime, n) be
$( 0!prime := false
1!prime := false
for i = 2 to n do i!prime := true
for p = 2 to isqrt(n) if p!prime
$( let c = p*p
while c<n
$( c!prime := false
c := c + p
$)
$)
$)
let square(n) = valof
$( let sq = isqrt(n)
resultis sq*sq = n
$)
let start() be
$( let prime = vec MAX
sieve(prime, MAX)
for i=2 to MAX if i!prime
$( let sq = i-1
if square(sq) then writef("%N ",sq)
$)
wrch('*N')
$)</syntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
=={{header|C}}==
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdbool.h>
#include <math.h>
#define MAX 1000
void sieve(int n, bool *prime) {
prime[0] = prime[1] = false;
for (int i=2; i<=n; i++) prime[i] = true;
for (int p=2; p*p<=n; p++)
if (prime[p])
for (int c=p*p; c<=n; c+=p) prime[c] = false;
}
bool square(int n) {
int sq = sqrt(n);
return (sq * sq == n);
}
int main() {
bool prime[MAX + 1];
sieve(MAX, prime);
for (int i=2; i<=MAX; i++) if (prime[i]) {
int sq = i-1;
if (square(sq)) printf("%d ", sq);
}
printf("\n");
return 0;
}</syntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
=={{header|CLU}}==
<syntaxhighlight lang="clu">isqrt = proc (s: int) returns (int)
x0: int := s/2
if x0=0 then return(s) end
x1: int := (x0 + s/x0)/2
while x1 < x0 do
x0 := x1
x1 := (x0 + s/x0)/2
end
return(x0)
end isqrt
sieve = proc (n: int) returns (array[int])
prime: array[bool] := array[bool]$fill(2,n-1,true)
primes: array[int] := array[int]$predict(1,isqrt(n))
for p: int in int$from_to(2,isqrt(n)) do
if prime[p] then
for c: int in int$from_to_by(p*p,n,p) do
prime[c] := false
end
end
end
for p: int in array[bool]$indexes(prime) do
if prime[p] then array[int]$addh(primes,p) end
end
return(primes)
end sieve
is_square = proc (n: int) returns (bool)
return(isqrt(n) ** 2 = n)
end is_square
start_up = proc ()
po: stream := stream$primary_output()
primes: array[int] := sieve(1000)
for prime: int in array[int]$elements(primes) do
n: int := prime-1
if is_square(n) then stream$puts(po, int$unparse(n) || " ") end
end
end start_up</syntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
=={{header|COBOL}}==
<syntaxhighlight lang="cobol"> IDENTIFICATION DIVISION.
PROGRAM-ID. SQUARE-PLUS-1-PRIME.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 N PIC 999.
01 P PIC 9999 VALUE ZERO.
01 PRIMETEST.
03 DSOR PIC 9999.
03 PRIME-FLAG PIC X.
88 PRIME VALUE '*'.
03 DIVTEST PIC 9999V999.
03 FILLER REDEFINES DIVTEST.
05 FILLER PIC 9999.
05 FILLER PIC 999.
88 DIVISIBLE VALUE ZERO.
PROCEDURE DIVISION.
BEGIN.
PERFORM CHECK-N VARYING N FROM 1 BY 1
UNTIL P IS GREATER THAN 1000.
STOP RUN.
CHECK-N.
MULTIPLY N BY N GIVING P.
ADD 1 TO P.
PERFORM CHECK-PRIME.
SUBTRACT 1 FROM P.
IF PRIME, DISPLAY P.
CHECK-PRIME.
IF P IS LESS THAN 2, MOVE SPACE TO PRIME-FLAG,
ELSE, MOVE '*' TO PRIME-FLAG.
PERFORM CHECK-DSOR VARYING DSOR FROM 2 BY 1
UNTIL NOT PRIME OR DSOR IS GREATER THAN N.
CHECK-DSOR.
DIVIDE P BY DSOR GIVING DIVTEST.
IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.</syntaxhighlight>
{{out}}
<pre>0001
0004
0016
0036
0100
0196
0256
0400
0576
0676</pre>
=={{header|Cowgol}}==
<syntaxhighlight lang="cowgol">include "cowgol.coh";
const MAX := 1000;
sub isqrt(s: uint16): (x0: uint16) is
x0 := s>>1;
if x0 == 0 then
x0 := s;
else
loop
var x1: uint16 := (x0 + s/x0) >> 1;
if x1 >= x0 then return; end if;
x0 := x1;
end loop;
end if;
end sub;
var prime: uint8[MAX + 1];
MemSet(&prime[0], 1, @bytesof prime);
var p: uint16 := 2;
while p*p <= MAX loop
if prime[p] != 0 then
var c := p*p;
while c <= MAX loop
prime[c] := 0;
c := c + p;
end loop;
end if;
p := p + 1;
end loop;
var i: uint16 := 2;
while i <= MAX loop
if prime[i] != 0 then
var sq := i - 1;
var sqr := isqrt(sq);
if sqr*sqr == sq then
print_i16(sq);
print_nl();
end if;
end if;
i := i + 1;
end loop;</syntaxhighlight>
{{out}}
<pre>1
4
16
36
100
196
256
400
576
676</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
function IsPrime(N: integer): boolean;
{Fast, optimised prime test}
var I,Stop: integer;
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));
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 ShowPrimeSquares(Memo: TMemo);
var N,S2: integer;
begin
for N:= 1 to Trunc(sqrt(1000-1)) do
begin
S2:=N*N;
if IsPrime(S2+1) then Memo.Text:=Memo.Text+' '+IntToStr(S2);
end;
end;
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|EasyLang}}==
<syntaxhighlight>
fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
n0 = 1
repeat
n = n0 * n0
until n >= 1000
if isprim (n + 1) = 1
write n & " "
.
n0 += 1
.
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]
<syntaxhighlight lang="fsharp">
// Find squares n where n+1 is prime. Nigel Galloway: December 17th., 2021
seq{yield 1; for g in 2..2..30 do let n=g*g in if isPrime(n+1) then yield n}|>Seq.iter(printf "%d "); printfn ""
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|Fermat}}==
<syntaxhighlight lang="fermat">!!1;
i:=2;
i2:=4;
while i2<1000 do
if Isprime(i2+1) then !!i2 fi;
i:+2;
i2:=i^2;
od;</syntaxhighlight>
{{out}}<pre>1
4
16
36
100
196
256
400
576
676
</pre>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">function isprime(n as integer) as boolean
if n<0 then return isprime(-n)
if n<2 then return false
if n<4 then return true
dim as uinteger i=3
while i*i<n
if n mod i = 0 then return false
i+=2
wend
return true
end function
print 1;" ";
dim as integer n=2, n2=4
while n2<1000
if isprime(1+n2) then print n2;" ";
n+=2
n2=n^2
wend</syntaxhighlight>
{{out}}<pre> 1 4 16 36 100 196 256 400 576 676</pre>
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"math"
"rcu"
)
func main() {
var squares []int
limit := int(math.Sqrt(1000))
i := 1
for i <= limit {
n := i * i
if rcu.IsPrime(n + 1) {
squares = append(squares, n)
}
if i == 1 {
i = 2
} else {
i += 2
}
}
fmt.Println("There are", len(squares), "square numbers 'n' where 'n+1' is prime, viz:")
fmt.Println(squares)
}</syntaxhighlight>
{{out}}
<pre>
There are 10 square numbers 'n' where 'n+1' is prime, viz:
[1 4 16 36 100 196 256 400 576 676]
</pre>
=={{header|GW-BASIC}}==
<syntaxhighlight lang="gwbasic">10 PRINT 1
20 N = 2 : N2 = 4
30 WHILE N2 < 1000
40 J = N2+1
50 GOSUB 110
60 IF PRIME = 1 THEN PRINT N2
70 N = N + 2
80 N2 = N*N
90 WEND
100 END
110 PRIME = 0
120 IF J < 2 THEN RETURN
130 PRIME = 1
140 IF J<4 THEN RETURN
150 I=5
160 WHILE I*I<J
170 IF J MOD I = 0 THEN PRIME = 0 : RETURN
180 I=I +2
190 WEND
200 RETURN</syntaxhighlight>
{{out}}<pre>1
4
16
36
100
196
256
400
576
676
</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">
module Squares
where
isPrime :: Int -> Bool
isPrime n
|n == 2 = True
|n == 1 = False
|otherwise = null $ filter (\i -> mod n i == 0 ) [2 .. root]
where
root :: Int
root = floor $ sqrt $ fromIntegral n
isSquare :: Int -> Bool
isSquare n = theFloor * theFloor == n
where
theFloor :: Int
theFloor = floor $ sqrt $ fromIntegral n
solution :: [Int]
solution = [d | d <- [1..999] , isSquare d && isPrime ( d + 1 )]
</syntaxhighlight>
{{out}}
<pre>
[1,4,16,36,100,196,256,400,576,676]
</pre>
=={{header|J}}==
<syntaxhighlight lang="j">((<.=])@%:#+)@(i.&.(p:^:_1)-1:) 1000</syntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
See [[Erdős-primes#jq]] for a suitable definition of `is_prime` as used here.
<syntaxhighlight lang="jq">def squares_for_which_successor_is_prime:
(. // infinite) as $limit
| {i:1, sq: 1}
| while( .sq < $limit; .i += 1 | .sq = .i*.i)
| .sq
| select((. + 1)|is_prime) ;
1000 | squares_for_which_successor_is_prime</syntaxhighlight>
{{out}}
<pre>
1
4
16
36
100
196
256
400
576
676
</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Primes
isintegersquarebeforeprime(n) = isqrt(n)^2 == n && isprime(n + 1)
foreach(p -> print(lpad(last(p), 5)), filter(isintegersquarebeforeprime, 1:1000))
</syntaxhighlight>{{out}}<pre> 1 4 16 36 100 196 256 400 576 676 </pre>
=={{header|MAD}}==
<syntaxhighlight lang="mad"> NORMAL MODE IS INTEGER
BOOLEAN PRIME
DIMENSION PRIME(1000)
INTERNAL FUNCTION(S)
ENTRY TO ISQRT.
X0 = S/2
WHENEVER X0.E.0, FUNCTION RETURN S
FNDRT X1 = (X0 + S/X0)/2
WHENEVER X1.GE.X0, FUNCTION RETURN X0
X0 = X1
TRANSFER TO FNDRT
END OF FUNCTION
THROUGH INIT, FOR P=2, 1, P.G.1000
INIT PRIME(P) = 1B
THROUGH SIEVE, FOR P=2, 1, P*P.G.1000
THROUGH SIEVE, FOR C=P*P, P, C.G.1000
SIEVE PRIME(C) = 0B
THROUGH TEST, FOR P=2, 1, P.G.1000
WHENEVER PRIME(P)
SQ = P-1
SQR = ISQRT.(SQ)
WHENEVER SQR*SQR.E.SQ
PRINT FORMAT FMT, SQ
END OF CONDITIONAL
END OF CONDITIONAL
TEST CONTINUE
VECTOR VALUES FMT = $I4*$
END OF PROGRAM</syntaxhighlight>
{{out}}
<pre> 1
4
16
36
100
196
256
400
576
676</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">Cases[Table[n^2, {n, 101}], _?(PrimeQ[# + 1] &)]</syntaxhighlight>
{{out}}<pre>
{1,4,16,36,100,196,256,400,576,676,1296,1600,2916,3136,4356,5476,7056,8100,8836}
</pre>
=={{header|Modula-2}}==
<syntaxhighlight lang="modula2">MODULE SquareAlmostPrime;
FROM InOut IMPORT WriteCard, WriteLn;
FROM MathLib IMPORT sqrt;
CONST Max = 1000;
VAR prime: ARRAY [0..Max] OF BOOLEAN;
i, sq: CARDINAL;
PROCEDURE Sieve;
VAR i, j, sqmax: CARDINAL;
BEGIN
sqmax := TRUNC(sqrt(FLOAT(Max)));
FOR i := 2 TO Max DO prime[i] := TRUE; END;
FOR i := 2 TO sqmax DO
IF prime[i] THEN
j := i * i;
WHILE j <= Max DO
prime[j] := FALSE;
j := j + i;
END;
END;
END;
END Sieve;
PROCEDURE isSquare(n: CARDINAL): BOOLEAN;
VAR sq: CARDINAL;
BEGIN
sq := TRUNC(sqrt(FLOAT(n)));
RETURN sq * sq = n;
END isSquare;
BEGIN
Sieve;
FOR i := 2 TO Max DO
IF prime[i] THEN
sq := i-1;
IF isSquare(sq) THEN
WriteCard(sq, 4);
WriteLn;
END;
END;
END;
END SquareAlmostPrime.</syntaxhighlight>
{{out}}
<pre> 1
4
16
36
100
196
256
400
576
676</pre>
=={{header|Nim}}==
<syntaxhighlight lang="Nim">import std/strutils
func isPrime(n: Positive): bool =
if n < 2: return false
if (n and 1) == 0: return n == 2
var d = 3
while d * d <= n:
if n mod d == 0:
return false
inc d, 2
result = true
var list = @[1]
var n = 2
var n2 = 4
while n2 < 1000:
if isPrime(n2 + 1):
list.add n2
inc n, 2
n2 = n * n
echo list.join(" ")
</syntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|OCaml}}==
<syntaxhighlight lang="ocaml">let is_prime n =
let rec test x =
x * x > n || n mod x <> 0 && n mod (x + 2) <> 0 && test (x + 6)
in if n < 5 then n lor 1 = 3 else n land 1 <> 0 && n mod 3 <> 0 && test 5
let seq_squares =
let rec next n a () = Seq.Cons (n, next (n + a) (a + 2)) in
next 0 1
let () =
let cond n = is_prime (succ n) in
seq_squares |> Seq.take_while ((>) 1000) |> Seq.filter cond
|> Seq.iter (Printf.printf " %u") |> print_newline</syntaxhighlight>
{{out}}
<pre> 1 4 16 36 100 196 256 400 576 676</pre>
=={{header|PARI/GP}}==
This is not terribly efficient, but it does show off the issquare and isprime functions.
<syntaxhighlight lang="parigp">for(n = 1, 1000, if(issquare(n)&&isprime(n+1),print(n)))</syntaxhighlight>
{{out}}<pre>1
4
16
36
100
196
256
400
576
676</pre>
=={{header|Perl}}==
===Simple and Clear===
<syntaxhighlight lang="perl">#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Find_squares_n_where_n%2B1_is_prime
use warnings;
use ntheory qw( primes is_square );
my @answer = grep is_square($_), map $_ - 1, @{ primes(1000) };
print "@answer\n";</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
===More Than One Way===
TMTOWTDI, right? So do it.
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
use ntheory 'is_prime';
my $a; is_prime $_ and $a = sqrt $_-1 and $a == int $a and say $_-1 for 1..1000; # backwards approach
my $b; do { say $b**2 if is_prime 1 + ++$b**2 } until $b > int sqrt 1000; # do/until
my $c; while (++$c < int sqrt 1000) { say $c**2 if is_prime 1 + $c**2 } # while/if
say for map $_**2, grep is_prime 1 + $_**2, 1 .. int sqrt 1000; # for/map/grep
for (1 .. int sqrt 1000) { say $_**2 if is_prime 1 + $_**2 } # for/if
say $_**2 for grep is_prime 1 + $_**2, 1 .. int sqrt 1000; # for/grep
is_prime 1 + $_**2 and say $_**2 for 1 .. int sqrt 1000; # and/for
is_prime 1+$_**2&&say$_**2for 1..31; # and/for golf, FTW
# or dispense with the module and find primes the slowest way possible
(1 x (1+$_**2)) !~ /^(11+)\1+$/ and say $_**2 for 1 .. int sqrt 1000;</syntaxhighlight>
{{out}}
In all cases:
<pre>1
4
16
36
100
196
256
400
576
676</pre>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">sq</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">sq</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1000</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sq</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">sq</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">4</span>
<span style="color: #000000;">sq</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">d</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{1,4,16,36,100,196,256,400,576,676}
</pre>
Alternative, same output, but 168 iterations/tests compared to just 16 by the above:
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">sq</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #004080;">integer</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">sq</span><span style="color: #0000FF;">))</span>
<!--</syntaxhighlight>-->
Drop the filter to get the 168 (cheekily humorous) squares-of-integers-and-non-integers result of Raku (and format/arrange them identically):
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #008000;">"%3d"</span><span style="color: #0000FF;">},</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)}),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">))</span>
<!--</syntaxhighlight>-->
=={{header|PL/M}}==
{{Trans|ALGOL W}}
{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator)
<syntaxhighlight lang="plm">
100H: /* FIND SQUARES N WHERE N + ! IS PRIME */
/* CP/M BDOS SYSTEM CALL AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* RETURNS TRUE IF N IS PRIME, FALSE OTHERWISE, USES TRIAL DIVISION */
IS$PRIME: PROCEDURE( N )BYTE;
DECLARE N ADDRESS;
DECLARE PRIME BYTE;
IF N < 3 THEN PRIME = N = 2;
ELSE IF N MOD 3 = 0 THEN PRIME = N = 3;
ELSE IF N MOD 2 = 0 THEN PRIME = 0;
ELSE DO;
DECLARE ( F, F2, TO$NEXT ) ADDRESS;
PRIME = 1;
F = 5;
F2 = 25;
TO$NEXT = 24; /* NOTE: ( 2N + 1 )^2 - ( 2N - 1 )^2 = 8N */
DO WHILE F2 <= N AND PRIME;
PRIME = N MOD F <> 0;
F = F + 2;
F2 = F2 + TO$NEXT;
TO$NEXT = TO$NEXT + 8;
END;
END;
RETURN PRIME;
END IS$PRIME;
/* TASK */
/* OTHER THAN 1, THE NUMBERS MUST BE EVEN */
IF IS$PRIME( 2 /* I.E.: ( 1 * 1 ) + 1 */ ) THEN DO;
CALL PR$CHAR( ' ' );
CALL PR$CHAR( '1' );
END;
DECLARE ( I2, TO$NEXT ) ADDRESS;
TO$NEXT, I2 = 4; /* NOTE: ( 2N + 2 )^2 - 2N^2 = 8N + 4 */
DO WHILE I2 < 1000;
IF IS$PRIME( I2 + 1 ) THEN DO;
CALL PR$CHAR( ' ' );
CALL PR$NUMBER( I2 );
END;
TO$NEXT = TO$NEXT + 8;
I2 = I2 + TO$NEXT;
END;
EOF
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|PROMAL}}==
{{Trans|ALGOL W}}
<syntaxhighlight lang="promal">
;;; Find squares n where n + 1 is prime
PROGRAM primesq
INCLUDE library
;;; returns TRUE(1) if p is prime, FALSE(0) otherwise
FUNC BYTE isPrime
ARG WORD n
WORD i
WORD f
WORD f2
WORD toNext
BYTE prime
BEGIN
IF n < 3
prime = n = 2
ELSE IF n % 3 = 0
prime = n = 3
ELSE IF n % 2 = 0
prime = 0
ELSE
prime = 1
f = 5
f2 = 25
toNext = 24 ; note: ( 2n + 1 )^2 - ( 2n - 1 )^2 = 8n
WHILE f2 <= n AND prime
prime = n % f <> 0
f = f + 2
f2 = toNext
toNext = toNext + 8
RETURN prime
END
WORD i2
WORD toNext
BEGIN
IF isPrime( ( 1 * 1 ) + 1 ) ; 1 is the only possible odd number
OUTPUT " 1"
i2 = 4
toNext = 4 ; note: ( 2n + 2 )^2 - 2n^2 = 8n + 4
WHILE i2 < 1000
IF isPrime( i2 + 1 )
OUTPUT " #W", i2
toNext = toNext + 8
i2 = i2 + toNext
END
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">
limit = 1000
print("working...")
def isprime(n):
for i in range(2,int(n**0.5)+1):
if n%i==0:
return False
return True
def issquare(x):
for n in range(1,x+1):
if (x == n*n):
return 1
return 0
for n in range(limit-1):
if issquare(n) and isprime(n+1):
print(n,end=" ")
print()
print("done...")
</syntaxhighlight>
{{out}}
<pre>
working...
1 4 16 36 100 196 256 400 576 676
done...
</pre>
=={{header|Quackery}}==
<code>isprime</code> is defined at [[Primality by trial division#Quackery]].
<syntaxhighlight lang="Quackery"> [] [] 0
[ 1+ dup 2 **
dup 1000 < while
1+ isprime if
[ dup dip join ]
again ]
2drop
witheach [ 2 ** join ]
echo</syntaxhighlight>
{{out}}
<pre>[ 1 4 16 36 100 196 256 400 576 676 ]</pre>
=={{header|Racket}}==
<syntaxhighlight lang="racket">
#lang racket
(define (find-subprime-squares up-to)
(let rc ([curr-num 1]
[found '()])
(let ([n-sq (* curr-num curr-num)])
(cond [(>= n-sq up-to) (reverse found)]
[(prime? (add1 n-sq)) (rc (add1 curr-num) (cons n-sq found))]
[else (rc (add1 curr-num) found)]))))
(define (prime? n)
(let iter ([counter 2])
(cond [(eq? n 1) #f]
[(<= (expt counter 2) n)
(if (zero? (remainder n counter))
#f
(iter (add1 counter)))]
[else #t])))
(find-subprime-squares 1000)
</syntaxhighlight>
{{out}}
<pre>
'(1 4 16 36 100 196 256 400 576 676)
</pre>
=={{header|Raku}}==
Use up to to one thousand (1,000) rather than up to one (1.000) as otherwise it would be a pretty short list...
<syntaxhighlight lang="raku"
{{out}}
<pre>(1 4 16 36 100 196 256 400 576 676)</pre>
Although, technically, there is absolutely nothing in the task directions specifying that '''n''' needs to be the square of an ''integer''. So, more accurately...
<syntaxhighlight lang="raku"
{{out}}
<pre> 1 2 4 6 10 12 16 18 22 28 30 36 40 42 46 52 58 60 66 70
Line 24 ⟶ 1,163:
=={{header|Ring}}==
<
load "stdlib.ring"
row = 0
Line 47 ⟶ 1,186:
next
return 0
</syntaxhighlight>
{{out}}
<pre>
Line 63 ⟶ 1,202:
Found 10 numbers
done...
</pre>
=={{header|RPL}}==
≪ { }
1 1000 √ '''FOR''' j
'''IF''' j SQ 1 + ISPRIME? '''THEN''' j SQ + '''END'''
'''NEXT'''
≫ '<span style="color:blue>TASK</span>' STO
{{out}}
<pre>
1: { 1 4 16 36 100 196 256 400 576 676 }
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
p (1..Integer.sqrt(1000)).filter_map{|n| sqr = n*n; sqr if (sqr+1).prime? }</syntaxhighlight>
{{out}}
<pre>
[1, 4, 16, 36, 100, 196, 256, 400, 576, 676]
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">
use primes::is_prime ;
fn is_square( number : u64 ) -> bool {
let floor : u64 = (number as f64).sqrt( ).floor( ) as u64 ;
floor * floor == number
}
fn main() {
let solution : Vec<u64> = (1..1000).into_iter( ).
filter( | d | is_square( *d ) && is_prime( *d + 1 )).collect( ) ;
println!("{:?}" , solution);
}
</syntaxhighlight>
{{out}}<pre>
[1, 4, 16, 36, 100, 196, 256, 400, 576, 676]
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">1..1000.isqrt -> map { _**2 }.grep { is_prime(_+1) }.say</syntaxhighlight>
{{out}}
<pre>
[1, 4, 16, 36, 100, 196, 256, 400, 576, 676]
</pre>
=={{header|Tiny BASIC}}==
<syntaxhighlight lang="tinybasic"> PRINT 1
LET N = 2
LET M = 4
10 LET J = M + 1
GOSUB 20
IF P = 1 THEN PRINT M
LET N = N + 2
LET M = N*N
IF M < 1000 THEN GOTO 10
END
20 LET P = 0
LET I = 3
30 IF (J/I)*I = J THEN RETURN
LET I = I + 2
IF I*I < J THEN GOTO 30
LET P = 1
RETURN</syntaxhighlight>
{{out}}<pre>1
4
16
36
100
196
256
400
576
676</pre>
=={{header|VTL-2}}==
{{Trans|TinyBASIC}}
<syntaxhighlight lang="vtl2">
1000 ?=1
1010 N=2
1020 M=4
1030 J=M+1
1040 #=2000
1050 #=P=1=0*1080
1060 $=32
1070 ?=M
1080 N=N+2
1090 M=N*N
1100 #=M<1000*1030
1110 #=9999
2000 R=!
2010 P=0
2020 I=3
2030 #=J/I*0+%=0*R
2040 I=I+2
2050 #=I*I<J*2030
2060 P=1
2070 #=R
</syntaxhighlight>
{{out}}
<pre>
1 4 16 36 100 196 256 400 576 676
</pre>
=={{header|Wren}}==
{{libheader|Wren-math}}
<
var squares = []
Line 78 ⟶ 1,321:
}
System.print("There are %(squares.count) square numbers 'n' where 'n+1' is prime, viz:")
System.print(squares)</
{{out}}
Line 87 ⟶ 1,330:
=={{header|XPL0}}==
<
int N, I;
[if N <= 2 then return N = 2;
Line 102 ⟶ 1,345:
if IsPrime(N*N+1) then
[IntOut(0, N*N); ChOut(0, ^ )];
]</
{{out}}
| |||