Working Strong Lucas test

lucas.py

@@ -1,6 +1,7 @@
 # Finding lucas pseudoprimes
 from math import sqrt, gcd, floor, log
 from time import process_time
+from psimp import trd, hund_div
 
 def isqrt(n):
     """ Find the integer square root of n via newton's method, code via
@@ -179,15 +180,75 @@ def LucasPrime(n):
     lnum = LucasFast(n + 1, 1, q, n)
     return lnum[0] == 0
 
+def StrongLucasPrime(n):
+    """Strong version of the Lucas probable prime test
+    """
+    if n < 2:
+        return False
+    if n == 2:
+        return True
+    if n % 2 == 0:
+        return False
+    d = FirstD(n)
+    if d == 0:
+        return False
+    s, od = trd(n + 1)
+    p = 1
+    q = (1 - d) // 4
+    uc, vc = Lucas(0, p, q)
+    dk = floor(log(od, 2))
+    tp = 2**dk
+    krunn = od
+    ks = 0
+    for i in range(dk + 1):
+        un = (uc * vc)
+        vn = (pow(vc, 2, n) - 2 * pow(q, ks, n))
+        uc = un % n
+        vc = vn % n
+        ks = ks * 2
+        if krunn >= tp:
+            krunn = krunn - tp
+            ks = ks + 1
+            un = p * uc + vc
+            if un % 2 != 0:
+                un = un + n
+            vn = (p * p - 4 * q) * uc + p * vc
+            if vn % 2 != 0:
+                vn = vn + n
+            uc = (un // 2) % n
+            vc = (vn // 2) % n
+        tp = tp // 2
+    if uc == 0:
+        return True
+    if vc == 0:
+        return True
+    for r in range(1, s):
+        un = (uc * vc)
+        vn = (pow(vc, 2, n) - 2 * pow(q, ks, n))
+        uc = un % n
+        vc = vn % n
+        if vc == 0:
+            return True
+        ks = ks * 2
+    return False
+
+
+
+#print(StrongLucasPrime(7))
 
 np = 0
 
-for i in range(1000):
-    lp = LucasPrime(i)
+for i in range(10000):
+    lp = StrongLucasPrime(i)
     if lp:
         np = np + 1
-    print("{}:\t{}".format(i, lp))
+        print("{}:\t{};\t{}".format(i, lp, np))
 
 print(np)
 
+print(StrongLucasPrime(5459))
+print(hund_div(5459))
+print(StrongLucasPrime(5777))
+print(hund_div(5777))
+