148 lines
2.7 KiB
Plaintext
148 lines
2.7 KiB
Plaintext
program Successive_prime_differences;
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{$APPTYPE CONSOLE}
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{$R *.res}
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uses
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System.SysUtils,
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System.Generics.Collections;
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function IsPrime(a: UInt64): Boolean;
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var
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d: UInt64;
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begin
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if (a < 2) then
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exit(False);
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if (a mod 2) = 0 then
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exit(a = 2);
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if (a mod 3) = 0 then
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exit(a = 3);
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d := 5;
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while (d * d <= a) do
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begin
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if (a mod d = 0) then
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Exit(false);
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inc(d, 2);
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if (a mod d = 0) then
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Exit(false);
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inc(d, 4);
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end;
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Result := True;
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end;
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function Primes(const limit: UInt64): TArray<UInt64>;
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var
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i: UInt64;
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procedure Add(const value: UInt64);
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begin
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SetLength(result, Length(result) + 1);
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Result[Length(result) - 1] := value;
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end;
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begin
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if limit < 2 then
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exit;
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// 2 is the only even prime
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Add(2);
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i := 3;
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while i <= limit do
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begin
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if IsPrime(i) then
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Add(i);
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inc(i, 2);
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end;
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end;
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function Commatize(const n: UInt64): string;
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var
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str: string;
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digits: Integer;
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i: Integer;
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begin
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Result := '';
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str := n.ToString;
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digits := str.Length;
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for i := 1 to digits do
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begin
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if ((i > 1) and (((i - 1) mod 3) = (digits mod 3))) then
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Result := Result + ',';
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Result := Result + str[i];
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end;
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end;
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function CheckScan(index: Integer; p: TArray<UInt64>; pattern: array of Integer): Boolean;
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var
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i, last: Integer;
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begin
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last := Length(pattern) - 1;
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for i := 0 to last do
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if p[index - last + i - 1] + pattern[i] <> p[index - last + i] then
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exit(False);
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Result := True;
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end;
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const
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GroupLabel: array[1..6] of string = ('(2)', '(1)', '(2, 2)', '(2, 4)',
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'(4, 2)', '(6, 4, 2)');
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var
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limit, start: UInt64;
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c: TArray<UInt64>;
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i, j: UInt64;
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Group: array[1..6] of Tlist<string>;
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begin
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for i := 1 to 6 do
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Group[i] := Tlist<string>.Create;
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limit := Trunc(1e6 - 1);
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c := Primes(limit);
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for j := 1 to High(c) do
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begin
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if CheckScan(j, c, [2]) then
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Group[1].Add(format('(%d,%d)', [c[j - 1], c[j]]));
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if CheckScan(j, c, [1]) then
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Group[2].Add(format('(%d,%d)', [c[j - 1], c[j]]));
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if j > 1 then
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begin
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if CheckScan(j, c, [2, 2]) then
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Group[3].Add(format('(%d,%d,%d)', [c[j - 2], c[j - 1], c[j]]));
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if CheckScan(j, c, [2, 4]) then
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Group[4].Add(format('(%d,%d,%d)', [c[j - 2], c[j - 1], c[j]]));
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if CheckScan(j, c, [4, 2]) then
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Group[5].Add(format('(%d,%d,%d)', [c[j - 2], c[j - 1], c[j]]));
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end;
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if j > 2 then
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if CheckScan(j, c, [6, 4, 2]) then
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Group[6].Add(format('(%d,%d,%d,%d)', [c[j - 3], c[j - 2], c[j - 1], c[j]]));
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end;
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for i := 1 to 6 do
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begin
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Write(GroupLabel[i], ': first group = ', Group[i].First);
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Writeln(', last group = ', Group[i].last, ', count = ', Group[i].Count);
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Group[i].free;
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end;
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readln;
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end.
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