Find prime numbers of the form n*n*n+2: Difference between revisions
Find prime numbers of the form n*n*n+2 (view source)
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n = 173 => n^3 + 2 = 5177719
n = 189 => n^3 + 2 = 6751271</pre>
=={{header|EasyLang}}==
<syntaxhighlight>
fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
for n = 1 to 199
p = pow n 3 + 2
if isprim p = 1
write p & " "
.
.
</syntaxhighlight>
{{out}}
<pre>
3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271
</pre>
=={{header|F_Sharp|F#}}==
Line 907 ⟶ 931:
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Find_prime_numbers_of_the_form_n%C2%B3%2B2}}
'''Solution'''
[[File:Fōrmulæ - Find prime numbers of the form n³ + 2 01.png]]
[[File:Fōrmulæ - Find prime numbers of the form n³ + 2 02.png]]
=={{header|Go}}==
Line 1,213 ⟶ 1,239:
173 5177719
189 6751271
</pre>
=={{header|Pascal}}==
==={{header|Free Pascal}}===
{{trans|Delphi}}
{{libheader| PrimTrial}}
<syntaxhighlight lang="pascal">
program Find_prime_numbers_of_the_form_n_n_n_plus_2;
{$IFDEF FPC}
{$MODE DELPHI} {$Optimization ON,ALL} {$COPERATORS ON}{$CODEALIGN proc=16}
{$ENDIF}
{$IFDEF WINDOWS}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
PrimTrial;
type
myString = String[31];
function Numb2USA(n:Uint64):myString;
const
//extend s by the count of comma to be inserted
deltaLength : array[0..24] of byte =
(0,0,0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7);
var
pI :pChar;
i,j : NativeInt;
Begin
str(n,result);
i := length(result);
//extend s by the count of comma to be inserted
// j := i+ (i-1) div 3;
j := i+deltaLength[i];
if i<> j then
Begin
setlength(result,j);
pI := @result[1];
dec(pI);
while i > 3 do
Begin
//copy 3 digits
pI[j] := pI[i];
pI[j-1] := pI[i-1];
pI[j-2] := pI[i-2];
// insert comma
pI[j-3] := ',';
dec(i,3);
dec(j,4);
end;
end;
end;
function n3_2(n:Uint32):Uint64;inline;
begin
n3_2 := UInt64(n)*n*n+2;
end;
const
limit =200;//trunc(exp(ln((HIGH(UInt32)-2))/3));
var
p : Uint64;
n : Uint32;
begin
n := 1;
repeat
p := n3_2(n);
if isPrime(p) then
writeln('n = ', Numb2USA(n):4, ' => n^3 + 2 = ', Numb2USA(p): 10);
inc(n,2);// n must be odd for n > 0
until n > Limit;
{$IFDEF WINDOWS}
readln;
{$IFEND}
end.</syntaxhighlight>
{{out}}
<pre>
n = 1 => n^3 + 2 = 3
n = 3 => n^3 + 2 = 29
n = 5 => n^3 + 2 = 127
n = 29 => n^3 + 2 = 24,391
n = 45 => n^3 + 2 = 91,127
n = 63 => n^3 + 2 = 250,049
n = 65 => n^3 + 2 = 274,627
n = 69 => n^3 + 2 = 328,511
n = 71 => n^3 + 2 = 357,913
n = 83 => n^3 + 2 = 571,789
n = 105 => n^3 + 2 = 1,157,627
n = 113 => n^3 + 2 = 1,442,899
n = 123 => n^3 + 2 = 1,860,869
n = 129 => n^3 + 2 = 2,146,691
n = 143 => n^3 + 2 = 2,924,209
n = 153 => n^3 + 2 = 3,581,579
n = 171 => n^3 + 2 = 5,000,213
n = 173 => n^3 + 2 = 5,177,719
n = 189 => n^3 + 2 = 6,751,271
</pre>
Line 1,360 ⟶ 1,482:
=={{header|Quackery}}==
<code>
<syntaxhighlight lang="Quackery"> [ dip number$
Line 1,369 ⟶ 1,491:
199 times
[ i^ 1+ 3 ** 2 +
dup
[ i^ 1+ 4 recho
sp 7 recho cr ]
Line 1,531 ⟶ 1,653:
</pre>
=={{header|RPL}}==
{{works with|HP|49g}}
≪ { }
1 200 '''FOR''' n
n 3 ^ 2 +
'''IF''' DUP ISPRIME? '''THEN''' + '''ELSE''' DROP '''END'''
'''NEXT'''
≫ '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: {3 29 127 24391 91127 250049 274627 328511 357913 571789 1157627 1442899 1860869 2146691 2924209 3581579 5000213 5177719 6751271}
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
p (1..200).filter_map{|n| cand = n**3 + 2; cand if cand.prime? }
</syntaxhighlight>
{{out}}
<pre>[3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271]</pre>
=={{header|Rust}}==
Line 1,713 ⟶ 1,855:
{{libheader|Wren-fmt}}
If ''n'' is even then ''n³ + 2'' is also even, so we only need to examine odd values of ''n'' here.
<syntaxhighlight lang="
import "./iterate" for Stepped
import "./fmt" for Fmt
var limit = 200
|