Data update

Task/Wieferich-primes/Python/wieferich-primes.py

@@ -1,27 +1,36 @@
-#!/usr/bin/python
+# Wieferich-Primzahlen
+MAX: int = 5_000
 
-def isPrime(n):
+# Berechnet a^n mod m
+def pow_mod(a: int, n: int, m: int) -> int:
+    assert n >= 0 and m != 0, "pow_mod(a, n, m), n >= 0, m <> 0"
+    res: int = 1
+    a %= m
+    while n > 0:
+        if n%2:
+            res = (res*a)%m
+            n -= 1
+        else:
+            a = (a*a)%m
+            n //= 2
+    return res%m
+
+def is_prime(n: int) -> bool:
     for i in range(2, int(n**0.5) + 1):
-        if n % i == 0:
+        if n%i == 0:
             return False
     return True
 
-def isWeiferich(p):
-    if not isPrime(p):
+def is_wieferich(p: int) -> True:
+    if is_prime(p) == False:
         return False
-    q = 1
-    p2 = p ** 2
-    while p > 1:
-        q = (2 * q) % p2
-        p -= 1
-    if q == 1:
+    if pow_mod(2, p - 1, p*p) == 1:
         return True
     else:
         return False
 
-
 if __name__ == '__main__':
-    print("Wieferich primes less than 5000: ")
-    for i in range(2, 5001):
-        if isWeiferich(i):
+    print(f"Wieferich primes less than {MAX}:")
+    for i in range(2, MAX + 1):
+        if is_wieferich(i):
             print(i)