Successive prime differences: Difference between revisions
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Last group = [997141, 997147, 997151, 997153]
Number found = 306</pre>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{libheader| System.Generics.Collections}}
<lang Delphi>
program Successive_prime_differences;
{$APPTYPE CONSOLE}
{$R *.res}
uses
System.SysUtils,
System.Generics.Collections;
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, 1); // all true except 1,2
FillChar(Result[0], sizeof(Boolean) * 2, 0); // 1,2 false
p := 3;
while true do
begin
p2 := p * p;
if p2 >= limit then
break;
i := p2;
while i < limit do
begin
Result[i] := false;
inc(i, 2 * p);
end;
while true do
begin
inc(p, 2);
if Result[p] then
Break;
end;
end;
// set False all even above 2
p := 4;
while p < limit do
begin
Result[p] := False;
inc(p, 2);
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;
const
GroupLabel: array[1..6] of string = ('(2)', '(1)', '(2, 2)', '(2, 4)',
'(4, 2)', '(6, 4, 2)');
var
limit, start: UInt64;
c: TArray<Boolean>;
i, j: UInt64;
Group: array[1..6] of Tlist<string>;
begin
for i := 1 to 6 do
Group[i] := Tlist<string>.Create;
limit := Trunc(1e6 - 1);
c := Sieve(limit);
start := 3;
j := start;
while j < limit do
begin
if c[j] and c[j - 2] then
Group[1].Add(format('(%d,%d)', [j - 2, j]));
if c[j] and c[j - 1] then
Group[2].Add(format('(%d,%d)', [j - 1, j]));
if (c[j - 2] and c[j]) and (c[j] and c[j + 2]) then
Group[3].Add(format('(%d,%d,%d)', [j - 2, j, j + 2]));
if (c[j - 2] and c[j]) and (c[j] and c[j + 4]) then
Group[4].Add(format('(%d,%d,%d)', [j - 2, j, j + 4]));
if j > 4 then
if (c[j - 4] and c[j]) and (c[j] and c[j + 2]) then
Group[5].Add(format('(%d,%d,%d)', [j - 4, j, j + 2]));
if j > 12 then
if (c[j - 12] and c[j-6]) and (c[j-6] and c[j -2]) and (c[j-2] and c[j]) then
Group[6].Add(format('(%d,%d,%d,%d)', [j - 12, j-6,j-2,j]));
inc(j);
end;
for i := 1 to 6 do
begin
Writeln(Group[i].Count);
Write(GroupLabel[i], ': first group = ', Group[i].First);
Writeln(', last group = ', Group[i].Last, ', count = ', Group[i].Count);
Group[i].free;
end;
readln;
end.
</lang>
{{out}}
<pre>
(2): first group = (3,5), last group = (999959,999961), count = 8169
(1): first group = (2,3), last group = (2,3), count = 1
(2, 2): first group = (3,5,7), last group = (3,5,7), count = 1
(2, 4): first group = (5,7,11), last group = (999431,999433,999437), count = 1393
(4, 2): first group = (7,11,13), last group = (997807,997811,997813), count = 1444
(6, 4, 2): first group = (7,13,17,19), last group = (997141,997147,997151,997153), count = 337
</pre>
=={{header|F_Sharp|F#}}==
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