Data update

Task/Blum-integer/AWK/blum-integer.awk

@@ -0,0 +1,53 @@
+# syntax: GAWK -f BLUM_INTEGER.AWK
+# converted from FutureBasic
+#
+# sorting:
+#   PROCINFO["sorted_in"] is used by GAWK
+#   SORTTYPE is used by Thompson Automation's TAWK
+#
+BEGIN {
+    n = 3
+    prime2 = 0
+    print("The first 50 Blum integers:")
+    while (1) {
+      if (is_semiprime(n)) {
+        if (prime1 % 4 == 3) {
+          prime2 = n / prime1
+          if ((prime2 != prime1) && (prime2 % 4 == 3)) {
+            arr[substr(n,length(n),1)]++
+            total++
+            if (++count <= 50) {
+              printf("%4d%s",n,count%10?"":"\n")
+            }
+            if (count ~ /^(26828|[1-4]00000)$/) {
+              printf("\nThe %6dth Blum integer: %7d",count,n)
+              if (count >= 400000) {
+                break
+              }
+            }
+          }
+        }
+      }
+      n += 2
+    }
+    PROCINFO["sorted_in"] = "@ind_num_asc" ; SORTTYPE = 1
+    printf("\n\nFor Blum integers up to %d:\n",count)
+    for (i in arr) {
+      printf("%7.3f%% end in %d\n",arr[i]/total*100,i)
+    }
+    exit(0)
+}
+function is_semiprime(n,  c,d) {
+    c = 0
+    d = 3
+    while (d * d <= n) {
+      while (n % d == 0) {
+        if (c == 2) { return(0) }
+        n /= d
+        c++
+      }
+      d += 2
+    }
+    prime1 = n
+    return(c == 1)
+}

Task/Blum-integer/Ada/blum-integer.adb

@@ -0,0 +1,89 @@
+with Ada.Text_IO; use Ada.Text_IO;
+with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
+with Ada.Float_Text_IO; use Ada.Float_Text_IO;
+
+procedure Blum is
+
+   Inc : Constant array (1 .. 8) of Integer := (4, 2, 4, 2, 4, 6, 2, 6);
+
+   function Is_Prime (N : Integer) return Boolean is
+      D : Integer := 5;
+   begin
+      if N < 2 then return False; end if;
+      if N mod 2 = 0 then return N = 2; end if;
+      if N mod 3 = 0 then return N = 3; end if;
+
+      while D * D <= N loop
+         if N mod D = 0 then return False; end if;
+	     D := D + 2;
+	     if N mod D = 0 then return False; end if;
+	     D := D + 4;
+      end loop;
+
+      return True;
+   end Is_Prime;
+
+   function First_Prime_Factor (N : Integer) return Integer is
+      D : Integer := 7;
+      I : Integer := 1;
+   begin
+      if N = 1 then return 1; end if;
+      if N mod 3 = 0 then return 3; end if;
+      if N mod 5 = 0 then return 5; end if;
+
+      while D * D <= N loop
+         if N mod D = 0 then
+            return D;
+	     end if;
+	     D := D + Inc(I);
+         I := (I mod 8) + 1;
+      end loop;
+
+      return N;
+   end First_Prime_Factor;
+
+   I, Blum_Count : Integer := 1;
+   J, P, Q : Integer;
+   Blums : Array (1 .. 50) of Integer;
+   Counts : Array (1 .. 4) of Integer := (others => 0);
+   Final_Digits : Array (1 .. 4) of Integer := (1, 3, 7, 9);
+
+begin
+   loop
+      P := First_Prime_Factor(I);
+      if P mod 4 = 3 then
+         Q := I / P;
+	     if Q /= P and Q mod 4 = 3 and Is_Prime(Q) then
+            if Blum_Count < 51 then Blums(Blum_Count) := I; end if;
+	        Counts(((I mod 10) / 3) + 1) := Counts(((I mod 10) / 3) + 1) + 1;
+	        Blum_Count := Blum_Count + 1;
+	        if Blum_Count = 51 then
+               Put("First 50 Blum Integers:"); New_Line;
+               for J in Integer range 1 .. 50 loop
+                  Put(Item => Blums(J), Width => 3); Put(" ");
+	              if J mod 10 = 0 then New_Line; end if;
+               end loop;
+	           New_Line;
+	        elsif Blum_Count = 26829 or Blum_Count mod 100000 = 1 then
+	           Put("The "); Put(Item => Blum_Count, Width => 7);
+               Put("th Blum Integer is: "); Put(Item => I, Width => 9);
+               New_Line;
+	           if Blum_Count = 400001 then
+		          New_Line; Put("% Distribution of the First 400,000 Blum Integers:"); New_Line;
+		          for J in Integer range 1 .. 4 loop
+		             Put("  "); Put(Item => Float(Counts(J)) / 4000.0, Fore => 2, Aft => 3, Exp => 0);
+                     Put("% end in "); Put(Item => Final_Digits(J), Width => 1);
+                     New_Line;
+		          end loop;
+		          exit;
+	           end if;
+	        end if;
+         end if;
+      end if;
+      if I mod 5 = 3 then
+         I := I + 4;
+      else
+	     I := I + 2;
+      end if;
+   end loop;
+end Blum;

Task/Blum-integer/Arturo/blum-integer.arturo

@@ -0,0 +1,17 @@
+blum?: function [n][
+    if any? @[n < 21, even? n, zero? n % 5]
+        -> return false
+
+    f: factors.prime n
+    if or? [2 <> size f][f\0 = f\1]
+        -> return false
+
+    every? f => [3 = & % 4]
+]
+
+print "First 50 Blum numbers:"
+1..∞ | select.first: 50 => blum?
+     | split.every: 10
+     | loop => [print map & 'x -> pad to :string x 4]
+
+print ["\n26828th Blum number:" select.n:26828 1..∞ => blum?]

Task/Blum-integer/Frink/blum-integer.frink

@@ -0,0 +1,27 @@
+isBlum = {|x|
+   f = factorFlat[x]
+   if length[f] != 2
+      return false
+
+   f1 = first[f]
+   f2 = last[f]
+   return (f1 != f2) and (first[f] mod 4 == 3) and (last[f] mod 4 == 3)
+}
+
+println["First 50:"]
+println[first[select[count[1], isBlum], 50]]
+
+ret = new array
+for n = [26828, 100000, 200000, 300000, 400000]
+   ret.push[["${n}th is: ", nth1[select[count[1], isBlum], n]]]
+
+println[formatTable[ret, "right"]]
+
+d = new dict
+for n = first[select[count[1], isBlum], 400000]
+   d.increment[right[toString[n],1]]
+
+println["Distribution of the first 400000 Blum integers:"]
+sum = sum[d.values[]]
+for k = sort[d.keys[]]
+   println[formatFix[d@k / sum, "percent", 3] + " end in $k"]

Task/Blum-integer/Pluto/blum-integer.pluto

@@ -0,0 +1,53 @@
+local int = require "int"
+local fmt = require "fmt"
+
+local inc = {4, 2, 4, 2, 4, 6, 2, 6}
+
+-- Assumes n is odd.
+local function first_prime_factor(n)
+    if n == 1     then return 1 end
+    if n % 3 == 0 then return 3 end
+    if n % 5 == 0 then return 5 end
+    local k = 7
+    local i = 1
+    while k * k <= n do
+        if n % k == 0 then
+            return k
+        else
+            k = k + inc[i]
+            i = i % 8 + 1
+        end
+    end
+    return n
+end
+
+local blum = {}
+local bc = 0
+local counts = { [1] = 0, [3] = 0, [7] = 0, [9] =  0 }
+local i = 1
+while true do
+    local p = first_prime_factor(i)
+    if p % 4 == 3 then
+        local q = i // p
+        if q != p and q % 4 == 3 and int.isprime(q) then
+            if bc < 50 then blum:insert(i) end
+            counts[i % 10] += 1
+            bc += 1
+            if bc == 50 then
+                print("First 50 Blum integers:")
+                fmt.tprint("%3d ", blum, 10)
+                print()
+            elseif bc == 26828 or bc % 100_000 == 0 then
+                fmt.print("The %9s Blum integer is: %9s", fmt.ord(bc, true), fmt.int(i))
+                if bc == 400_000 then
+                    print("\n% distribution of the first 400,000 Blum integers:")
+                    for {1, 3, 7, 9} as j do
+                        fmt.print("  %6.3f%% end in %d", counts[j] / 4000, j)
+                    end
+                    return
+                end
+            end
+        end
+    end
+    i = (i % 5 == 3) ? i + 4 : i + 2
+end

Task/Blum-integer/REXX/blum-integer-1.rexx

@@ -0,0 +1,59 @@
+include Setting
+
+Say Time()
+Call Time 'R'
+blumCount = 0
+blums.=0
+lastDigitCounts.=0
+Do number=5 By 4 While blumCount < 400000
+  Prime=leastPrimeFactor(number)
+  If Prime // 4=3 Then Do
+    quotient=number / Prime;
+    If quotient <> Prime & isPrimeType3(quotient) Then Do
+       blumCount+=1
+       If blumCount<=50 Then Do
+        blums.blumCount=number
+        End
+      lastdigit=Right(number,1)
+      lastDigitCounts.lastdigit+=1
+      If blumCount=50 Then Do
+        Say "The first 50 Blum integers:"
+        Do i=1 To 50
+          If Right(i,1)=1 Then
+            l=Format(blums.i,3)
+          Else
+            l=l Format(blums.i,3)
+          If i//10=0 Then
+            Say l
+          End
+        Say ''
+        End
+      Else Do
+        If blumCount=26828 | blumCount // 100000 = 0 Then Do
+          Say "The " Format(blumCount,7)"th Blum Integer is:" Format(number,7) Time()
+          If blumCount=400000 Then Do
+            Say ''
+            Say "Percent distribution of the first 400000 Blum integers:"
+            Do i=0 To 9
+              If lastDigitCounts.i>0 Then
+                Say Format(lastDigitCounts.i/4000,6,3)'% end in' i
+              End
+            End
+          End
+        End
+      End
+    End
+  End
+Say Time()
+say Time('E') 'seconds'
+Exit
+
+isPrimeType3: Procedure expose Memo.
+  Parse Arg number
+  Return Prime(number) & (number//4=3)
+
+leastPrimeFactor: Procedure expose Memo.
+  Parse Arg number
+  Return FFactor(number)
+
+include Math

Task/Blum-integer/REXX/blum-integer-2.rexx

@@ -0,0 +1,89 @@
+-- 28 Aug 2025
+include Setting
+arg count
+if count = '' then
+   count = 400000
+threshold=25*count
+
+say 'BLUM INTEGER'
+say version
+say
+say 'Parameters...'
+say 'Threshold' threshold 'Count' count
+say
+say 'Collect primes...'
+say Primes(threshold) 'found'; say
+say 'Filter primes 3 modulo 4...'
+say Filter3Mod4() 'found'; say
+say 'Generate Blum integers...'
+say GenerateBlum(threshold) 'found'; say
+say 'Blum integers...'; say
+call Results threshold,count
+call Timer
+exit
+
+Filter3Mod4:
+procedure expose Prim.
+n=0
+do i = 1 to Prim.0
+   if Prim.i//4 = 3 then
+      n=n+1
+   else
+      Prim.i=0
+end
+return n
+
+GenerateBlum:
+procedure expose Prim. Blum.
+arg threshold
+Blum.=0; n=0
+do i = 1 to Prim.0
+   if Prim.i <> 0 then do
+      do j = i+1 to Prim.0
+         if Prim.j <> 0 then do
+            p=Prim.i*Prim.j
+            if p > threshold then
+               leave j
+            n=n+1; Blum.p=1
+         end
+      end
+   end
+end
+return n
+
+Results:
+procedure expose Blum.
+arg threshold,count
+n=0; digs.=0
+do i = 5 by 4 to threshold
+   if \ Blum.i then
+      iterate i
+   n=n+1
+   if n > count then
+      leave i
+   d=Right(i,1); digs.d=digs.d+1
+   if n < 51 then do
+      if n = 1 then
+         say 'The first 50 are'
+      call CharOut ,Right(i,4)
+      if n//10 = 0 then
+         say
+      if n = 50 then
+         say
+      iterate i
+   end
+   if n = 26828 | n//100000 = 0 then
+      say 'The' n'th is' i
+   if n = count then do
+      say
+      say 'Percent distribution of the first' count
+      do i = 1 to 9
+         if digs.i > 0 then
+            say format(digs.i*100/count,2,3)'% ends in' i
+      end
+   end
+end
+say
+return 0
+
+include Math