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Find squares n where n+1 is prime: Difference between revisions

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Find squares n where n+1 is prime (view source)

Revision as of 12:59, 27 August 2022

994 bytes added ,  1 year ago
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=={{header|ALGOL 68}}==
{{libheader|ALGOL 68-primes}}
<langsyntaxhighlight 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 #
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FI
OD
END</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|AutoHotkey}}==
{{trans|FreeBASIC}}
<langsyntaxhighlight AutoHotkeylang="autohotkey">n := 0
while ((n2 := (n+=2)**2) < 1000)
if isPrime(n2+1)
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return False
return True
}</langsyntaxhighlight>
{{out}}
<pre>1, 4, 16, 36, 100, 196, 256, 400, 576, 676</pre>
 
=={{header|AWK}}==
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f FIND_SQUARES_N_WHERE_N+1_IS_PRIME.AWK
BEGIN {
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return(1)
}
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{header|BASIC}}==
<langsyntaxhighlight lang="basic">10 DEFINT A-Z: N=1000
20 DIM C(N)
30 FOR P=2 TO SQR(N)
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80 X=I-1: R=SQR(X)
90 IF R*R=X THEN PRINT X;
100 NEXT</langsyntaxhighlight>
{{out}}
<pre> 1 4 16 36 100 196 256 400 576 676</pre>
 
=={{header|BCPL}}==
<langsyntaxhighlight lang="bcpl">get "libhdr"
manifest $( MAX = 1000 $)
 
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$)
wrch('*N')
$)</langsyntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
 
=={{header|C}}==
<langsyntaxhighlight lang="c">#include <stdio.h>
#include <stdbool.h>
#include <math.h>
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printf("\n");
return 0;
}</langsyntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
 
=={{header|CLU}}==
<langsyntaxhighlight lang="clu">isqrt = proc (s: int) returns (int)
x0: int := s/2
if x0=0 then return(s) end
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if is_square(n) then stream$puts(po, int$unparse(n) || " ") end
end
end start_up</langsyntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
 
=={{header|COBOL}}==
<langsyntaxhighlight lang="cobol"> IDENTIFICATION DIVISION.
PROGRAM-ID. SQUARE-PLUS-1-PRIME.
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CHECK-DSOR.
DIVIDE P BY DSOR GIVING DIVTEST.
IF DIVISIBLE, MOVE SPACE TO PRIME-FLAG.</langsyntaxhighlight>
{{out}}
<pre>0001
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=={{header|Cowgol}}==
<langsyntaxhighlight lang="cowgol">include "cowgol.coh";
 
const MAX := 1000;
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end if;
i := i + 1;
end loop;</langsyntaxhighlight>
{{out}}
<pre>1
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=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]
<langsyntaxhighlight 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>
</lang>
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<pre>
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=={{header|Fermat}}==
<langsyntaxhighlight lang="fermat">!!1;
i:=2;
i2:=4;
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i:+2;
i2:=i^2;
od;</langsyntaxhighlight>
{{out}}<pre>1
4
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=={{header|FreeBASIC}}==
<langsyntaxhighlight lang="freebasic">function isprime(n as integer) as boolean
if n<0 then return isprime(-n)
if n<2 then return false
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n+=2
n2=n^2
wend</langsyntaxhighlight>
{{out}}<pre> 1 4 16 36 100 196 256 400 576 676</pre>
 
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{{trans|Wren}}
{{libheader|Go-rcu}}
<langsyntaxhighlight lang="go">package main
 
import (
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fmt.Println("There are", len(squares), "square numbers 'n' where 'n+1' is prime, viz:")
fmt.Println(squares)
}</langsyntaxhighlight>
 
{{out}}
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=={{header|GW-BASIC}}==
<langsyntaxhighlight lang="gwbasic">10 PRINT 1
20 N = 2 : N2 = 4
30 WHILE N2 < 1000
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180 I=I +2
190 WEND
200 RETURN</langsyntaxhighlight>
{{out}}<pre>1
4
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=={{header|J}}==
<langsyntaxhighlight lang="j">((<.=])@%:#+)@(i.&.(p:^:_1)-1:) 1000</langsyntaxhighlight>
{{out}}
<pre>1 4 16 36 100 196 256 400 576 676</pre>
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See [[Erdős-primes#jq]] for a suitable definition of `is_prime` as used here.
 
<langsyntaxhighlight lang="jq">def squares_for_which_successor_is_prime:
(. // infinite) as $limit
| {i:1, sq: 1}
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| select((. + 1)|is_prime) ;
 
1000 | squares_for_which_successor_is_prime</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Julia}}==
<langsyntaxhighlight lang="julia">using Primes
 
isintegersquarebeforeprime(n) = isqrt(n)^2 == n && isprime(n + 1)
 
foreach(p -> print(lpad(last(p), 5)), filter(isintegersquarebeforeprime, 1:1000))
</langsyntaxhighlight>{{out}}<pre> 1 4 16 36 100 196 256 400 576 676 </pre>
 
=={{header|MAD}}==
<langsyntaxhighlight MADlang="mad"> NORMAL MODE IS INTEGER
BOOLEAN PRIME
DIMENSION PRIME(1000)
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VECTOR VALUES FMT = $I4*$
END OF PROGRAM</langsyntaxhighlight>
{{out}}
<pre> 1
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676</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<langsyntaxhighlight Mathematicalang="mathematica">Cases[Table[n^2, {n, 101}], _?(PrimeQ[# + 1] &)]</langsyntaxhighlight>
{{out}}<pre>
{1,4,16,36,100,196,256,400,576,676,1296,1600,2916,3136,4356,5476,7056,8100,8836}
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=={{header|Modula-2}}==
<langsyntaxhighlight lang="modula2">MODULE SquareAlmostPrime;
FROM InOut IMPORT WriteCard, WriteLn;
FROM MathLib IMPORT sqrt;
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END;
END;
END SquareAlmostPrime.</langsyntaxhighlight>
{{out}}
<pre> 1
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This is not terribly efficient, but it does show off the issquare and isprime functions.
 
<langsyntaxhighlight lang="parigp">for(n = 1, 1000, if(issquare(n)&&isprime(n+1),print(n)))</langsyntaxhighlight>
 
{{out}}<pre>1
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=={{header|Perl}}==
===Simple and Clear===
<langsyntaxhighlight lang="perl">#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Find_squares_n_where_n%2B1_is_prime
use warnings;
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my @answer = grep is_square($_), map $_ - 1, @{ primes(1000) };
print "@answer\n";</langsyntaxhighlight>
{{out}}
<pre>
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===More Than One Way===
TMTOWTDI, right? So do it.
<langsyntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
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# or dispense with the module and find primes the slowest way possible
(1 x (1+$_**2)) !~ /^(11+)\1+$/ and say $_**2 for 1 .. int sqrt 1000;</langsyntaxhighlight>
{{out}}
In all cases:
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=={{header|Phix}}==
<!--<langsyntaxhighlight Phixlang="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>
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<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>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
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</pre>
Alternative, same output, but 168 iterations/tests compared to just 16 by the above:
<!--<langsyntaxhighlight Phixlang="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>
<!--</langsyntaxhighlight>-->
Drop the filter to get the 168 (cheekily humorous) squares-of-integers-and-non-integers result of Raku (and format/arrange them identically):
<!--<langsyntaxhighlight Phixlang="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>
<!--</langsyntaxhighlight>-->
 
=={{header|Python}}==
<langsyntaxhighlight lang="python">
limit = 1000
print("working...")
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print()
print("done...")
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{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" perl6line>say ({$++²}…^*>Ⅿ).grep: (*+1).is-prime</langsyntaxhighlight>
{{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" perl6line>put (^Ⅿ).grep(*.is-prime).map(*-1).batch(20)».fmt("%3d").join: "\n"</langsyntaxhighlight>
{{out}}
<pre> 1 2 4 6 10 12 16 18 22 28 30 36 40 42 46 52 58 60 66 70
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=={{header|Ring}}==
<langsyntaxhighlight lang="ring">
load "stdlib.ring"
row = 0
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next
return 0
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{header|Sidef}}==
<langsyntaxhighlight lang="ruby">1..1000.isqrt -> map { _**2 }.grep { is_prime(_+1) }.say</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Tiny BASIC}}==
<langsyntaxhighlight lang="tinybasic"> PRINT 1
LET N = 2
LET M = 4
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IF I*I < J THEN GOTO 30
LET P = 1
RETURN</langsyntaxhighlight>
{{out}}<pre>1
4
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=={{header|Wren}}==
{{libheader|Wren-math}}
<langsyntaxhighlight lang="ecmascript">import "./math" for Int
 
var squares = []
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}
System.print("There are %(squares.count) square numbers 'n' where 'n+1' is prime, viz:")
System.print(squares)</langsyntaxhighlight>
 
{{out}}
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=={{header|XPL0}}==
<langsyntaxhighlight XPL0lang="xpl0">func IsPrime(N); \Return 'true' if N is prime
int N, I;
[if N <= 2 then return N = 2;
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if IsPrime(N*N+1) then
[IntOut(0, N*N); ChOut(0, ^ )];
]</langsyntaxhighlight>
 
{{out}}
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