Twin primes: Difference between revisions
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Maximum: 10000000
twin prime pairs below 10000000: 58980
</pre>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{Trans|Wren}}
<lang Delphi>
program Primes;
{$APPTYPE CONSOLE}
{$R *.res}
uses
System.SysUtils;
function IsPrime(a: UInt64): Boolean;
var
d: UInt64;
begin
if (a < 2) then
exit(False);
if (a mod 2) = 0 then
exit(a = 2);
if (a mod 3) = 0 then
exit(a = 3);
d := 5;
while (d * d <= a) do
begin
if (a mod d = 0) then
Exit(false);
inc(d, 2);
if (a mod d = 0) then
Exit(false);
inc(d, 4);
end;
Result := True;
end;
function Sieve(limit: UInt64): TArray<Boolean>;
var
p, p2, i: UInt64;
begin
inc(limit);
SetLength(Result, limit);
FillChar(Result[2], sizeof(Boolean) * limit - 2, 0); // all false except 1,2
FillChar(Result[0], sizeof(Boolean) * 2, 1); // 1,2 are true
p := 3;
while true do
begin
p2 := p * p;
if p2 >= limit then
break;
i := p2;
while i < limit do
begin
Result[i] := true;
inc(i, 2 * p);
end;
while true do
begin
inc(p, 2);
if not Result[p] then
Break;
end;
end;
end;
function Commatize(const n: UInt64): string;
var
str: string;
digits: Integer;
i: Integer;
begin
Result := '';
str := n.ToString;
digits := str.Length;
for i := 1 to digits do
begin
if ((i > 1) and (((i - 1) mod 3) = (digits mod 3))) then
Result := Result + ',';
Result := Result + str[i];
end;
end;
var
limit, start, twins: UInt64;
c: TArray<Boolean>;
i, j: UInt64;
begin
c := Sieve(Trunc(1e9 - 1));
limit := 10;
start := 3;
twins := 0;
for i := 1 to 9 do
begin
j := start;
while j < limit do
begin
if (not c[j]) and (not c[j - 2]) then
inc(twins);
inc(j, 2);
end;
Writeln(Format('Under %14s there are %10s pairs of twin primes.', [commatize
(limit), commatize(twins)]));
start := limit + 1;
limit := 10 * limit;
end;
readln;
end.
</lang>
{{out}}
<pre>
Under 10 there are 2 pairs of twin primes.
Under 100 there are 8 pairs of twin primes.
Under 1,000 there are 35 pairs of twin primes.
Under 10,000 there are 205 pairs of twin primes.
Under 100,000 there are 1,224 pairs of twin primes.
Under 1,000,000 there are 8,169 pairs of twin primes.
Under 10,000,000 there are 58,980 pairs of twin primes.
Under 100,000,000 there are 440,312 pairs of twin primes.
Under 1,000,000,000 there are 3,424,506 pairs of twin primes.
</pre>
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