Find prime numbers of the form n*n*n+2: Difference between revisions

</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