Data update

Task/Blum-integer/FreeBASIC/blum-integer.basic

@@ -1,39 +1,76 @@
-Dim Shared As Uinteger Prime1
-Dim As Uinteger n = 3, c = 0, Prime2
+#include "isprime.bas"
 
-Function isSemiprime(n As Uinteger) As Boolean
-    Dim As Uinteger d = 3, c = 0
-    While d*d <= n
-        While n Mod d = 0
-            If c = 2 Then Return False
-            n /= d
-            c += 1
-        Wend
-        d += 2
-    Wend
-    Prime1 = n
-    Return c = 1
+Type PrimeHelper
+    inc(7) As Integer
+    idx As Integer
+End Type
+
+Function initPrimeHelper() As PrimeHelper
+    Dim helper As PrimeHelper
+    helper.inc(0) = 4 : helper.inc(1) = 2 : helper.inc(2) = 4
+    helper.inc(3) = 2 : helper.inc(4) = 4 : helper.inc(5) = 6
+    helper.inc(6) = 2 : helper.inc(7) = 6
+    helper.idx = 0
+    Return helper
 End Function
 
-Print "The first 50 Blum integers:"
-Do
-    If isSemiprime(n) Then
-        If Prime1 Mod 4 = 3 Then
-            Prime2 = n / Prime1
-            If (Prime2 <> Prime1) And (Prime2 Mod 4 = 3) Then
-                c += 1
-                If c <= 50 Then
-                    Print Using "####"; n;
-                    If c Mod 10 = 0 Then Print
-                End If
-                If c >= 26828 Then
-                    Print !"\nThe 26828th Blum integer is: " ; n
-                    Exit Do
+Function firstPrimeFactor(n As Integer) As Integer
+    If n = 1 Then Return 1
+    If n Mod 3 = 0 Then Return 3
+    If n Mod 5 = 0 Then Return 5
+
+    Dim helper As PrimeHelper = initPrimeHelper()
+    Dim k As Integer = 7
+
+    While k * k <= n
+        If n Mod k = 0 Then Return k
+        k += helper.inc(helper.idx)
+        helper.idx = (helper.idx + 1) Mod 8
+    Wend
+
+    Return n
+End Function
+
+Sub main()
+    Dim As Integer blum(49), counts(9)
+    Dim As Integer bc = 0, i = 1, p, q
+    Dim As Integer j
+
+    Dim As Double t0 = Timer
+    Do
+        p = firstPrimeFactor(i)
+        If p Mod 4 = 3 Then
+            q = i \ p
+            If q <> p Andalso q Mod 4 = 3 Andalso isPrime(q) Then
+                If bc < 50 Then blum(bc) = i
+                counts(i Mod 10) += 1
+                bc += 1
+
+                If bc = 50 Then
+                    Print "First 50 Blum integers:"
+                    For j = 0 To 49
+                        Print Using "####"; blum(j);
+                        If (j + 1) Mod 10 = 0 Then Print
+                    Next
+                    Print
+                Elseif bc = 26828 Orelse bc Mod 100000 = 0 Then
+                    Print Using "The ###,###th Blum integer is: #,###,###"; bc; i
+
+                    If bc = 400000 Then
+                        Print !"\n% distribution of the first 400,000 Blum integers:"
+                        For j = 1 To 9 Step 2
+                            If j <> 5 Then Print Using "  ##.###% end in #"; (counts(j)/4000); j
+                        Next
+                        Exit Do
+                    End If
                 End If
             End If
         End If
-    End If
-    n += 2
-Loop
+        i += Iif(i Mod 5 = 3, 4, 2)
+    Loop
+    Print Chr(10); Timer - t0; " sec."
+End Sub
+
+main()
 
 Sleep