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Quadrat special primes: Difference between revisions

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Quadrat special primes (view source)

Revision as of 12:07, 29 January 2024

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{{trans|Nim}}
 
<langsyntaxhighlight lang="11l">F is_prime(n)
I n == 2
R 1B
Line 35:
print(‘Quadrat special primes < 16000:’)
L(qp) quadraPrimes
print(‘#5’.format(qp), end' I (L.index + 1) % 7 == 0 {"\n"} E ‘ ’)</langsyntaxhighlight>
 
{{out}}
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=={{header|Action!}}==
{{libheader|Action! Sieve of Eratosthenes}}
<langsyntaxhighlight Actionlang="action!">INCLUDE "H6:SIEVE.ACT"
 
DEFINE MAX="15999"
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p=FindNextQuadraticPrime(p)
OD
RETURN</langsyntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Quadrat_Special_Primes.png Screenshot from Atari 8-bit computer]
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{{Trans|ALGOL W}}
{{libheader|ALGOL 68-primes}}
<langsyntaxhighlight lang="algol68">BEGIN # find some primes where the gap between the current prime and the next is a square #
# an array of squares #
PROC get squares = ( INT n )[]INT:
Line 132:
DO sq pos +:= 2 OD
OD
END</langsyntaxhighlight>
{{out}}
<pre>
Line 143:
 
=={{header|ALGOL W}}==
<langsyntaxhighlight lang="algolw">begin % find some primes where the gap between the current prime and the next is a square %
% sets p( 1 :: n ) to a sieve of primes up to n %
procedure Eratosthenes ( logical array p( * ) ; integer value n ) ;
Line 185:
end while_thisPrime_lt_MAX_NUMBER
end
end.</langsyntaxhighlight>
{{out}}
<pre>
Line 195:
</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f QUADRAT_SPECIAL_PRIMES.AWK
# converted from FreeBASIC
Line 228:
return(1)
}
</syntaxhighlight>
</lang>
{{out}}
<pre>
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==={{header|Applesoft BASIC}}===
{{trans|BASIC256}}
<langsyntaxhighlight lang="gwbasic"> 100 FOR P = 2 TO 16000
110 PRINT S$P;
120 LET S$ = " "
Line 264:
290 IF NOT ISPRIME THEN RETURN
300 NEXT D
310 RETURN</langsyntaxhighlight>
==={{header|BASIC256}}===
<langsyntaxhighlight BASIC256lang="basic256">function isPrime(v)
if v < 2 then return False
if v mod 2 = 0 then return v = 2
Line 291:
j = 1
end while
end</langsyntaxhighlight>
 
==={{header|PureBasic}}===
<langsyntaxhighlight PureBasiclang="purebasic">Procedure isPrime(v.i)
If v <= 1 : ProcedureReturn #False
ElseIf v < 4 : ProcedureReturn #True
Line 333:
ForEver
Input()
CloseConsole()</langsyntaxhighlight>
 
==={{header|Yabasic}}===
<langsyntaxhighlight lang="yabasic">sub isPrime(v)
if v < 2 then return False : fi
if mod(v, 2) = 0 then return v = 2 : fi
Line 361:
j = 1
loop
end</langsyntaxhighlight>
 
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="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 QuadratSpecialPrimes(Memo: TMemo);
var Q,P,Cnt: integer;
var IA: TIntegerDynArray;
begin
Memo.Lines.Add('Count Prime1 Prime2 Gap Sqrt');
Memo.Lines.Add('---------------------------------');
Cnt:=0;
Q:=2;
for P:=3 to 16000-1 do
if IsPrime(P) then
begin
if frac(sqrt(P - Q))=0 then
begin
Inc(Cnt);
Memo.Lines.Add(Format('%5D%7D%8D%7D%6.1f',[Cnt,Q,P,P-Q,Sqrt(P-Q)]));
Q:=P;
end;
end;
Memo.Lines.Add('Count = '+IntToStr(Cnt));
end;
 
 
</syntaxhighlight>
{{out}}
<pre>
Count Prime1 Prime2 Gap Sqrt
---------------------------------
1 2 3 1 1.0
2 3 7 4 2.0
3 7 11 4 2.0
4 11 47 36 6.0
5 47 83 36 6.0
6 83 227 144 12.0
7 227 263 36 6.0
8 263 587 324 18.0
9 587 911 324 18.0
10 911 947 36 6.0
11 947 983 36 6.0
12 983 1019 36 6.0
13 1019 1163 144 12.0
14 1163 1307 144 12.0
15 1307 1451 144 12.0
16 1451 1487 36 6.0
17 1487 1523 36 6.0
18 1523 1559 36 6.0
19 1559 2459 900 30.0
20 2459 3359 900 30.0
21 3359 4259 900 30.0
22 4259 4583 324 18.0
23 4583 5483 900 30.0
24 5483 5519 36 6.0
25 5519 5843 324 18.0
26 5843 5879 36 6.0
27 5879 6203 324 18.0
28 6203 6779 576 24.0
29 6779 7103 324 18.0
30 7103 7247 144 12.0
31 7247 7283 36 6.0
32 7283 7607 324 18.0
33 7607 7643 36 6.0
34 7643 8219 576 24.0
35 8219 8363 144 12.0
36 8363 10667 2304 48.0
37 10667 11243 576 24.0
38 11243 11279 36 6.0
39 11279 11423 144 12.0
40 11423 12323 900 30.0
41 12323 12647 324 18.0
42 12647 12791 144 12.0
43 12791 13367 576 24.0
44 13367 13691 324 18.0
45 13691 14591 900 30.0
46 14591 14627 36 6.0
47 14627 14771 144 12.0
48 14771 15671 900 30.0
Count = 48
Elapsed Time: 111.233 ms.
</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">
//Quadrat special primes. Nigel Galloway: January 16th., 2023
let isPs(n:int)=MathNet.Numerics.Euclid.IsPerfectSquare n
let rec fG n g=seq{match Seq.tryHead g with Some h when isPs(h-n)->yield h; yield! fG h g |Some _->yield! fG n g |_->()}
fG 2 (primes32()|>Seq.takeWhile((>)16000))|>Seq.iter(printf "%d "); printfn ""
</syntaxhighlight>
{{out}}
<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
=={{header|Factor}}==
{{works with|Factor|0.98}}
<langsyntaxhighlight lang="factor">USING: fry io kernel lists lists.lazy math math.primes prettyprint ;
 
2 [ 1 lfrom swap '[ sq _ + ] lmap-lazy [ prime? ] lfilter car ]
lfrom-by [ 16000 < ] lwhile [ pprint bl ] leach nl</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|FreeBASIC}}==
<langsyntaxhighlight lang="freebasic">
#include "isprime.bas"
 
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loop
print
</syntaxhighlight>
</lang>
{{out}}
<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
 
=={{header|FutureBasic}}==
<syntaxhighlight lang="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 QuadratSpecialPrimes
NSUInteger p = 2, j = 1, count = 1
printf @"%6lu \b", 2
while (1)
count++
while (1)
if fn IsPrime( p + j*j ) then exit while
j += 1
wend
p += j*j
if p > 16000 then exit while
printf @"%6lu \b", p
if count == 7 then count = 0 : print
j = 1
wend
print
end fn
 
fn QuadratSpecialPrimes
 
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
2 3 7 11 47 83 227
263 587 911 947 983 1019 1163
1307 1451 1487 1523 1559 2459 3359
4259 4583 5483 5519 5843 5879 6203
6779 7103 7247 7283 7607 7643 8219
8363 10667 11243 11279 11423 12323 12647
12791 13367 13691 14591 14627 14771 15671
</pre>
 
=={{header|Go}}==
{{trans|Wren}}
<langsyntaxhighlight lang="go">package main
 
import (
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}
fmt.Println("\n", count+1, "such primes found.")
}</langsyntaxhighlight>
 
{{out}}
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=={{header|J}}==
<langsyntaxhighlight Jlang="j">{{
j=. 0
r=. 2
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end.
}} p:i.p:inv 16e3
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671</langsyntaxhighlight>
=={{header|jq}}==
'''Adaptation of [[#Julia|Julia]]
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For the definition of `is_prime` used here, see https://rosettacode.org/wiki/Additive_primes
<syntaxhighlight lang="jq">
<lang jq>
# Input: a number > 2
# Output: an array of the quadrat primes less than `.`
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"Quadrat special primes < 16000:",
(16000 | quadrat[])
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{header|Julia}}==
<langsyntaxhighlight lang="julia">using Primes
 
function quadrat(N = 16000)
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println("Quadrat special primes < 16000:")
foreach(p -> print(rpad(p[2], 6), p[1] % 10 == 0 ? "\n" : ""), enumerate(quadrat()))
</langsyntaxhighlight>{{out}}
<pre>
Quadrat special primes < 16000:
Line 561 ⟶ 727:
 
=={{header|Ksh}}==
<langsyntaxhighlight lang="ksh">
#!/bin/ksh
 
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done
printf "\n"
</syntaxhighlight>
</lang>
{{out}}<pre>
2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
Line 619 ⟶ 785:
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<langsyntaxhighlight Mathematicalang="mathematica">ps = {2};
Do[
Do[
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];
ps //= Most;
Multicolumn[ps, {Automatic, 7}, Appearance -> "Horizontal"]</langsyntaxhighlight>
{{out}}
<pre>2 3 7 11 47 83 227
Line 645 ⟶ 811:
8363 10667 11243 11279 11423 12323 12647
12791 13367 13691 14591 14627 14771 15671</pre>
 
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
quadrat(n):=block(aux:next_prime(n),while not integerp(sqrt(aux-n)) do aux:next_prime(aux),aux)$
block(a:2,append([a],makelist(a:quadrat(a),48)));
</syntaxhighlight>
{{out}}
<pre>
[2,3,7,11,47,83,227,263,587,911,947,983,1019,1163,1307,1451,1487,1523,1559,2459,3359,4259,4583,5483,5519,5843,5879,6203,6779,7103,7247,7283,7607,7643,8219,8363,10667,11243,11279,11423,12323,12647,12791,13367,13691,14591,14627,14771,15671]
</pre>
 
=={{header|Nim}}==
<langsyntaxhighlight Nimlang="nim">import math, strutils, sugar
 
func isPrime(n: Natural): bool =
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for qp in quadraPrimes(Max):
inc count
stdout.write ($qp).align(5), if count mod 7 == 0: '\n' else: ' '</langsyntaxhighlight>
 
{{out}}
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=={{header|Perl}}==
{{libheader|ntheory}}
<langsyntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
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} until $sp[-1] >= 16000;
 
pop @sp and say ((sprintf '%-7d'x@sp, @sp) =~ s/.{1,$#sp}\K\s/\n/gr);</langsyntaxhighlight>
{{out}}
<pre>2 3 7 11 47 83 227
Line 723 ⟶ 899:
 
=={{header|Phix}}==
<!--<langsyntaxhighlight Phixlang="phix">(phixonline)-->
<span style="color: #008080;">constant</span> <span style="color: #000000;">desc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"linear quadratic cubic quartic quintic sextic septic octic nonic decic"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">limits</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: #000000;">16000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">15000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">14e9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8025e5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25e12</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">195e12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">75e11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3e9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11e8</span><span style="color: #0000FF;">}</span>
Line 745 ⟶ 921:
<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;">"Found %d %s special primes &lt; %g:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">],</span><span style="color: #000000;">N</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
Line 786 ⟶ 962:
 
=={{header|Python}}==
<langsyntaxhighlight lang="python">#!/usr/bin/python
 
def isPrime(n):
Line 808 ⟶ 984:
break
print(p, end = " ");
j = 1</langsyntaxhighlight>
 
=={{header|Raku}}==
 
<syntaxhighlight lang="raku" perl6line>my @sqp = 2, -> $previous {
my $next;
for (1..∞).map: *² {
Line 822 ⟶ 998:
 
say "{+$_} matching numbers:\n", $_».fmt('%5d').batch(7).join: "\n" given
@sqp[^(@sqp.first: * > 16000, :k)];</langsyntaxhighlight>
{{out}}
<pre>49 matching numbers:
Line 834 ⟶ 1,010:
 
=={{header|REXX}}==
<langsyntaxhighlight lang="rexx">/*REXX program finds the smallest primes such that the difference of successive terms */
/*─────────────────────────────────────────────────── are the smallest quadrat numbers. */
parse arg hi cols . /*obtain optional argument from the CL.*/
Line 883 ⟶ 1,059:
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
Line 899 ⟶ 1,075:
 
=={{header|Ring}}==
<langsyntaxhighlight lang="ring">load "stdlib.ring"
/* Searching for the smallest prime gaps under a limit,
Line 942 ⟶ 1,118:
s = string(x) l = len(s)
if l > y y = l ok
return substr(" ", 11 - y + l) + s</langsyntaxhighlight>
{{out}}
<pre style="height:20em">working...
Line 1,070 ⟶ 1,246:
 
done...</pre>
 
=={{header|RPL}}==
{{works with|HP|49}}
≪ <span style="color:red">{ 2 } 2</span> DUP
'''DO'''
DUP NEXTPRIME
'''IF''' DUP2 SWAP - √ FP NOT '''THEN''' NIP SWAP OVER + SWAP DUP '''END'''
'''UNTIL''' DUP <span style="color:red">16000</span> ≥ '''END'''
DROP2
≫ '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: {2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671}
</pre>
Runs in 6 minutes 25 seconds on a HP-50g.
 
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
 
res = [2]
 
until res.last > 16000 do
res << (1..).detect{|n| (res.last + n**2).prime? } ** 2 + res.last
end
 
puts res[..-2].join(" ")
</syntaxhighlight>
{{out}}
<pre>2 3 7 11 47 83 227 263 587 911 947 983 1019 1163 1307 1451 1487 1523 1559 2459 3359 4259 4583 5483 5519 5843 5879 6203 6779 7103 7247 7283 7607 7643 8219 8363 10667 11243 11279 11423 12323 12647 12791 13367 13691 14591 14627 14771 15671
</pre>
 
=={{header|Sidef}}==
<langsyntaxhighlight lang="ruby">func quadrat_primes(callback) {
 
var prev = 2
Line 1,089 ⟶ 1,295:
take(k)
})
}</langsyntaxhighlight>
{{out}}
<pre>
Line 1,098 ⟶ 1,304:
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<langsyntaxhighlight ecmascriptlang="wren">import "./math" for Int
import "./fmt" for Fmt
 
var isSquare = Fn.new { |n|
Line 1,121 ⟶ 1,327:
}
}
System.print("\n%(count+1) such primes found.")</langsyntaxhighlight>
 
{{out}}
Line 1,181 ⟶ 1,387:
=={{header|XPL0}}==
Find primes where the difference between the current one and a following one is a perfect square.
<langsyntaxhighlight XPL0lang="xpl0">func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
Line 1,206 ⟶ 1,412:
Text(0, " such primes found below 16000.
");
]</langsyntaxhighlight>
 
{{out}}
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