Flake lucas.py

lucas.py

@@ -1,8 +1,7 @@
 # Finding lucas pseudoprimes
-from math import sqrt, gcd, floor, log
-from time import process_time
-from psimp import trd, hund_div
-from sieve import sieve
+from math import gcd, floor, log
+from psimp import trd
+
 
 def isqrt(n):
     """ Find the integer square root of n via newton's method, code via
@@ -17,6 +16,7 @@ def isqrt(n):
         y = (x + n // x) // 2
     return x
 
+
 def hasIntSQRT(n):
     """Detect whether the square root of n is an integer,
     i.e. whether the isqrt(n) is the true square root.
@@ -24,6 +24,7 @@ def hasIntSQRT(n):
     isq = isqrt(n)
     return isq * isq == n
 
+
 def Dsequence():
     """Generate sequence 5, -7, 9, -11, 13, -15...
     """
@@ -35,6 +36,7 @@ def Dsequence():
             yield -val
         val = val + 2
 
+
 def Legendre(a, p):
     """Function for calculating Legendre symbol.
 
@@ -47,11 +49,12 @@ def Legendre(a, p):
     """
     if (p % 2 == 0):
         raise ValueError("p must be odd, is {}".format(p))
-    lv =  pow(a, (p-1)//2, p)
+    lv = pow(a, (p-1)//2, p)
     if lv == p - 1:
         lv = -1
     return lv
 
+
 def Jacobi(a, n):
     """Function for calculating Jacobi symbol.
 
@@ -65,7 +68,7 @@ def Jacobi(a, n):
     if (n % 2 == 0):
         raise ValueError("n must be odd")
     if a % n != a:
-        return Jacobi(a%n, n)
+        return Jacobi(a % n, n)
     if a != 0 and a % 2 == 0:
         nm8 = n % 8
         if (nm8 == 3 or nm8 == 5):
@@ -82,6 +85,7 @@ def Jacobi(a, n):
         return -1 * Jacobi(n, a)
     return Jacobi(n, a)
 
+
 def FirstD(n):
     """Return first D in the sequence 5, -7, 9, -11, 13, -15... for which the
     Jacobi symbol (D/n) is -1. Returns 0 if the number is a perfect square, or
@@ -107,6 +111,7 @@ def FirstD(n):
     # Shouldn't fire
     return 0
 
+
 def Lucas(n, p, q):
     """Function for generating values of a lucas sequence with parameters p, q.
     Via formula at <https://en.wikipedia.org/wiki/Lucas_sequence>
@@ -122,6 +127,7 @@ def Lucas(n, p, q):
         Vc = Vn
     return Uc, Vc
 
+
 def LucasUn(n, p, q):
     """Return only the U numbers from a lucas sequence Un(P, Q). For example if
     P = 1, and Q = -1 this will return the Fibonacci numbers; if P = 3 and Q =
@@ -129,6 +135,7 @@ def LucasUn(n, p, q):
     """
     return Lucas(n, p, q)[0]
 
+
 def LucasVn(n, p, q):
     """Return only V numbers from a local sequence Vn(P, Q).
     """
@@ -169,6 +176,7 @@ def LucasFast(k, p, q, n):
         tp = tp // 2
     return(uc, vc)
 
+
 def LucasPrime(n):
     """Lucas probable prime test
     (note: not the "strong" test.)
@@ -186,6 +194,7 @@ 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
     """
@@ -237,15 +246,3 @@ def StrongLucasPrime(n):
             return True
         ks = ks * 2
     return False
-
-
-
-mp = 400000
-ap = sieve(mp)
-for i in range(mp):
-    iip = i in ap
-    lp = StrongLucasPrime(i)
-    if iip != lp:
-        print(iip, lp, i, hund_div(i), sep='\t')
-
-