some math scripts

Cryptography/tools/finding_if_prime.py

@@ -0,0 +1,57 @@
+#!/usr/bin/python
+
+import math
+import random
+
+def finding_prime(number):
+    ''' find whether a number is prime in a simple way'''
+    num = abs(number)
+    if num < 4 : return True
+    for x in range(2, num):
+        if num % x == 0:
+            return False
+    return True
+       
+
+def finding_prime_sqrt(number):
+    ''' find whether a number is prime as soon as it rejects all candidates up to sqrt(n) '''
+    num = abs(number)
+    if num < 4 : return True
+    for x in range(2, int(math.sqrt(num)) + 1):
+        if number % x == 0:
+            return False
+    return True
+
+
+def finding_prime_fermat(number):
+    ''' find whether a number is prime with Fermat's theorem, using probabilistic tests '''
+    if number <= 102:
+        for a in range(2, number):
+            if pow(a, number- 1, number) != 1:
+                return False
+        return True
+    else:
+        for i in range(100):
+            a = random.randint(2, number - 1)
+            if pow(a, number - 1, number) != 1:
+                return False
+        return True
+
+
+
+def test_finding_prime():
+    number1 = 17
+    number2 = 20
+    assert(finding_prime(number1) == True)
+    assert(finding_prime(number2) == False)
+    assert(finding_prime_sqrt(number1) == True)
+    assert(finding_prime_sqrt(number2) == False)
+    assert(finding_prime_fermat(number1) == True)
+    assert(finding_prime_fermat(number2) == False)
+    print('Tests passed!')
+
+
+if __name__ == '__main__':
+    test_finding_prime()
+
+