Rosetta Code

De Polignac numbers: Difference between revisions

Page Discussion

De Polignac numbers (view source)

Revision as of 00:49, 4 February 2024

7,775 bytes added ,  3 months ago
Add Mathematica/Wolfram Language implementation
(Added BASIC256 and Chipmunk Basic)
(Add Mathematica/Wolfram Language implementation)
 
(7 intermediate revisions by 6 users not shown)
Line 673:
1,000th = 31,941
10,000th = 273,421
</pre>
 
=={{header|EasyLang}}==
{{trans|C}}
<syntaxhighlight lang=easylang>
func isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
p = 2
for i to 20
pow2[] &= p
p *= 2
.
n = 1
while count < 50
j = 1
repeat
p = pow2[j]
until p > n or isprim (n - p) = 1
j += 1
.
if p > n
count += 1
print n
.
n += 2
.
</syntaxhighlight>
 
=={{header|Euler}}==
Basic task only.<br/>
Based on the Algol W sample, but as 3 is clearly not a de Polignac number, only considers odd primes.
'''begin''' '''new''' isOddPrime;
isOddPrime
&lt;- ` '''formal''' n;
'''if''' n '''mod''' 2 = 0
'''then''' '''false'''
'''else''' '''begin'''
'''new''' prime; '''new''' f; '''new''' f2; '''new''' toNext; '''label''' primeLoop;
prime &lt;- '''true''';
f &lt;- 3;
f2 &lt;- 9;
toNext &lt;- 16;
primeLoop: '''if''' f2 &lt;= n '''and''' prime '''then''' '''begin'''
prime &lt;- n '''mod''' f &lt;&gt; 0;
f &lt;- f + 2;
f2 &lt;- toNext;
toNext &lt;- toNext + 8;
'''goto''' primeLoop '''end''' '''else''' 0;
prime
'''end'''
&apos;;
'''begin''' '''new''' n; '''new''' count; '''label''' forI;
count &lt;- 0;
n &lt;- -1;
forI: '''if''' '''begin''' n &lt;- n + 2; count &lt; 50 '''end''' '''then''' '''begin'''
'''new''' found; '''new''' p; '''new''' powerOf2; '''label''' p2Loop;
found &lt;- '''false''';
powerOf2 &lt;- 1;
p2Loop: '''if''' '''not''' found '''and''' n &gt; powerOf2 '''then''' '''begin'''
found &lt;- isOddPrime( n - powerOf2 );
powerOf2 &lt;- powerOf2 * 2;
'''goto''' p2Loop '''end''' '''else''' 0;
'''if''' '''not''' found '''then''' '''begin'''
count &lt;- count + 1;
'''out''' n
'''end''' '''else''' 0;
'''goto''' forI '''end''' '''else''' 0
'''end'''
'''end''' $
 
{{out}}
<pre>
NUMBER 1
NUMBER 127
NUMBER 149
...
NUMBER 2171
NUMBER 2203
NUMBER 2213
</pre>
 
Line 816 ⟶ 904:
273421</syntaxhighlight>
(We use 999 here for the 1000th number because 0 is the first J index.)
 
=={{header|Java}}==
<syntaxhighlight lang="java">
public final class DePolignacNumbers {
 
public static void main(String[] args) {
System.out.println("The first 50 de Polignac numbers:");
for ( int n = 1, count = 0; count < 10_000; n += 2 ) {
if ( isDePolignacNumber(n) ) {
count += 1;
if ( count <= 50 ) {
System.out.print(String.format("%5d%s", n, ( count % 10 == 0 ? "\n" : " ") ));
} else if ( count == 1_000 ) {
System.out.println();
System.out.println("The 1,000th de Polignac number: " + n);
} else if ( count == 10_000 ) {
System.out.println();
System.out.println("The 10,000th de Polignac number: " + n);
}
}
}
}
private static boolean isDePolignacNumber(int number) {
for ( int p = 1; p < number; p <<= 1 ) {
if ( isPrime(number - p) ) {
return false;
}
}
return true;
}
private static boolean isPrime(int number) {
if ( number < 2 ) {
return false;
}
if ( number % 2 == 0 ) {
return number == 2;
}
if ( number % 3 == 0 ) {
return number == 3;
}
int delta = 2;
int k = 5;
while ( k * k <= number ) {
if ( number % k == 0 ) {
return false;
}
k += delta;
delta = 6 - delta;
}
return true;
}
}
</syntaxhighlight>
{{ out }}
<pre>
The first 50 de Polignac numbers:
1 127 149 251 331 337 373 509 599 701
757 809 877 905 907 959 977 997 1019 1087
1199 1207 1211 1243 1259 1271 1477 1529 1541 1549
1589 1597 1619 1649 1657 1719 1759 1777 1783 1807
1829 1859 1867 1927 1969 1973 1985 2171 2203 2213
 
The 1,000th de Polignac number: 31941
 
The 10,000th de Polignac number: 273421
</pre>
 
=={{header|jq}}==
Line 954 ⟶ 1,112:
 
The 10000th de Polignac number is 273421
</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
{{trans|Julia}}
<syntaxhighlight lang="Mathematica">
IsDePolignac[n_Integer] := Module[{twoPows},
If[EvenQ[n], Return[False]];
twoPows = 2^Range[0, Floor[Log2[n]]];
Not[Or @@ (PrimeQ[n - #] & /@ twoPows)]
]
 
DePolignacs[] := Module[{naturals = 1},
Select[Table[naturals++, {i, 1, 280000}], IsDePolignac]
]
 
dePolignacNumbers = DePolignacs[];
 
Print["The first 50 de Polignac numbers:", Take[dePolignacNumbers, 50]];
 
Print["The 1000th de Polignac number is ", dePolignacNumbers[[1000]]];
 
Print["The 10000th de Polignac number is ", dePolignacNumbers[[10000]]];
</syntaxhighlight>
{{out}}
<pre>
The first 50 de Polignac numbers:{1, 127, 149, 251, 331, 337, 373, 509, 599, 701, 757, 809, 877, 905, 907, 959, 977, 997, 1019, 1087, 1199, 1207, 1211, 1243, 1259, 1271, 1477, 1529, 1541, 1549, 1589, 1597, 1619, 1649, 1657, 1719, 1759, 1777, 1783, 1807, 1829, 1859, 1867, 1927, 1969, 1973, 1985, 2171, 2203, 2213}
The 1000th de Polignac number is 31941
The 10000th de Polignac number is 273421
 
</pre>
 
Line 1,144 ⟶ 1,331:
{{libheader|ntheory}}
<syntaxhighlight lang="perl" line>use v5.36;
use bigint;
use ntheory <is_prime vecmax vecany logint>;
 
Line 1,153 ⟶ 1,339:
while ($n++) {
next unless $n % 2;
next if vecany { is_prime($n - 2**(1 << $_)) } reverse(1 .. logint ($n, 2));
push @D, comma $n;
last if 10_000 == @D;
Line 1,504 ⟶ 1,690:
 
10000: 273421
</pre>
 
=={{header|Scala}}==
{{trans|Java}}
<syntaxhighlight lang="Scala">
object DePolignacNumbers extends App {
 
println("The first 50 de Polignac numbers:")
Stream.from(1, 2).filter(isDePolignacNumber).take(10000).zipWithIndex.foreach {
case (number, index) =>
val count = index + 1
if (count <= 50) {
print(f"$number%5d" + (if (count % 10 == 0) "\n" else " "))
} else if (count == 1000) {
println()
println(s"The 1,000th de Polignac number: $number")
} else if (count == 10000) {
println()
println(s"The 10,000th de Polignac number: $number")
}
}
 
def isDePolignacNumber(number: Int): Boolean = {
Iterator.iterate(1)(_ << 1).takeWhile(_ < number).forall(p => !isPrime(number - p))
}
 
def isPrime(number: Int): Boolean = number match {
case n if n < 2 => false
case 2 | 3 => true
case n if n % 2 == 0 || n % 3 == 0 => false
case _ =>
Stream.from(5, 2).takeWhile(k => k * k <= number)
.filter(k => number % k == 0 || number % (k + 2) == 0)
.isEmpty
}
 
}
</syntaxhighlight>
{{out}}
<pre>
The first 50 de Polignac numbers:
1 127 149 251 331 337 373 509 599 701
757 809 877 905 907 959 977 997 1019 1087
1199 1207 1211 1243 1259 1271 1477 1529 1541 1549
1589 1597 1619 1649 1657 1719 1759 1777 1783 1807
1829 1859 1867 1927 1969 1973 1985 2171 2203 2213
 
The 1,000th de Polignac number: 31941
 
The 10,000th de Polignac number: 273421
</pre>
 
 
=={{header|Sidef}}==
{{trans|Ruby}}
<syntaxhighlight lang="ruby">var polignacs = (1..Inf -> by(2).lazy.grep {|n|
RangeNum(n.ilog2, 0, -1).none {|k| n - (1<<k) -> is_prime }
})
 
with (50) {|n|
say ("first #{n} de Polignac numbers:")
polignacs.first(n).slices(10).each{|s| say("%5d"*s.len % s...) }
}
 
say ''; [1000, 10000].each{|n|
say "#{n}th de Polignac number: #{polignacs.nth(n)}"
}</syntaxhighlight>
{{out}}
<pre>
first 50 de Polignac numbers:
1 127 149 251 331 337 373 509 599 701
757 809 877 905 907 959 977 997 1019 1087
1199 1207 1211 1243 1259 1271 1477 1529 1541 1549
1589 1597 1619 1649 1657 1719 1759 1777 1783 1807
1829 1859 1867 1927 1969 1973 1985 2171 2203 2213
 
1000th de Polignac number: 31941
10000th de Polignac number: 273421
</pre>
 
Line 1,509 ⟶ 1,773:
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./math" for Int
import "./fmt" for Fmt
 
Aspen138
337

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/358210...358218"