Data update

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