Successive prime differences: Difference between revisions

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@@ Line 472: / Line 472: @@
 end;
-function Sieve(limit: UInt64): TArray<Boolean>;
+function Primes(const limit: UInt64): TArray<UInt64>;
 var
-  p, p2, i: UInt64;
+  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
+  procedure Add(const value: UInt64);
-  p := 3;
-  while true do
   begin
+    SetLength(result, Length(result) + 1);
-    p2 := p * p;
+    Result[Length(result) - 1] := value;
-    if p2 >= limit then
-      break;
+  end;
+begin
-    i := p2;
-    while i < limit do
+  if limit < 2 then
-    begin
+    exit;
-      Result[i] := false;
-      inc(i, 2 * p);
-    end;
+  // 2 is the only even prime
-    while true do
-    begin
+  Add(2);
-      inc(p, 2);
-      if Result[p] then
-        Break;
-    end;
-  end;
+  i := 3;
-  // set False all even above 2
-  p := 4;
+  while i <= limit do
-  while p < limit do
   begin
+    if IsPrime(i) then
-    Result[p] := False;
-    inc(p, 2);
+      Add(i);
+    inc(i, 2);
   end;
 end;
@@ Line 528: / Line 514: @@
     Result := Result + str[i];
   end;
+end;
+function CheckScan(index: Integer; p: TArray<UInt64>; pattern: array of Integer): Boolean;
+var
+  i, last: Integer;
+begin
+  last := Length(pattern) - 1;
+  for i := 0 to last do
+    if p[index - last + i - 1] + pattern[i] <> p[index - last + i] then
+      exit(False);
+  Result := True;
 end;
@@ Line 536: / Line 533: @@
 var
   limit, start: UInt64;
-  c: TArray<Boolean>;
+  c: TArray<UInt64>;
   i, j: UInt64;
   Group: array[1..6] of Tlist<string>;
@@ Line 545: / Line 542: @@
   limit := Trunc(1e6 - 1);
-  c := Sieve(limit);
+  c := Primes(limit);
-  start := 3;
+  for j := 1 to High(c) do
-  j := start;
-  while j < limit do
   begin
-    if c[j] and c[j - 2] then
+    if CheckScan(j, c, [2]) then
-      Group[1].Add(format('(%d,%d)', [j - 2, j]));
+      Group[1].Add(format('(%d,%d)', [c[j - 1], c[j]]));
-    if c[j] and c[j - 1] then
+    if CheckScan(j, c, [1]) then
-      Group[2].Add(format('(%d,%d)', [j - 1, j]));
+      Group[2].Add(format('(%d,%d)', [c[j - 1], c[j]]));
-    if (c[j - 2] and c[j]) and (c[j] and c[j + 2]) then
+    if j > 1 then
+    begin
-      Group[3].Add(format('(%d,%d,%d)', [j - 2, j, j + 2]));
+      if CheckScan(j, c, [2, 2]) then
+        Group[3].Add(format('(%d,%d,%d)', [c[j - 2], c[j - 1], c[j]]));
-    if (c[j - 2] and c[j]) and (c[j] and c[j + 4]) then
+      if CheckScan(j, c, [2, 4]) then
-      Group[4].Add(format('(%d,%d,%d)', [j - 2, j, j + 4]));
+        Group[4].Add(format('(%d,%d,%d)', [c[j - 2], c[j - 1], c[j]]));
-    if j > 4 then
+      if CheckScan(j, c, [4, 2]) then
-      if (c[j - 4] and c[j]) and (c[j] and c[j + 2]) then
+        Group[5].Add(format('(%d,%d,%d)', [c[j - 2], c[j - 1], c[j]]));
+    end;
-        Group[5].Add(format('(%d,%d,%d)', [j - 4, j, j + 2]));
-    if j > 12 then
+    if j > 2 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
+      if CheckScan(j, c, [6, 4, 2]) then
-        Group[6].Add(format('(%d,%d,%d,%d)', [j - 12, j-6,j-2,j]));
+        Group[6].Add(format('(%d,%d,%d,%d)', [c[j - 3], c[j - 2], c[j - 1], c[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);
+    Writeln(', last group = ', Group[i].last, ', count = ', Group[i].Count);
     Group[i].free;
   end;
   readln;
 end.
@@ Line 596: / Line 589: @@
 (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
+(6, 4, 2): first group = (31,37,41,43), last group = (997141,997147,997151,997153), count = 306
 </pre>