Merge pull request #34 from 0awawa0/fermat_test

Added fermat_test.md

contributor_database

@@ -27,4 +27,5 @@ bubble_sort: [Shobhit Sachan](@sachans)
 has_duplicates: [Rob-Rychs](@Rob-Rychs)
 keys_only: [Rob-Rychs](@Rob-Rychs),[Matteo Veraldi](@mattveraldi)
 values_only: [Rob-Rychs](@Rob-Rychs)
-all_unique: [Rob-Rychs](@Rob-Rychs)
+all_unique: [Rob-Rychs](@Rob-Rychs)
+fermat_test: [Alexander Pozdniakov](@0awawa0)

snippets/fermat_test.md

@@ -0,0 +1,33 @@
+### fermat_test
+
+Checks if the number is prime or not. Returns True if passed number is prime, and False if not.
+
+The function uses Fermat's theorem. 
+First, it picks the number `A` in range `1`..`(n-1)`, then it checks if `A` to the power of `n-1` modulo `n` equals `1`. 
+If not, the number is not prime, else it's pseudoprime with probability 1/2. Applying this test `k `times we have probability `1/(2^k)`.
+For example, if the number passes the test `10` times, we have probability `0.00098`.
+
+``` python
+from random import randint
+
+
+def fermat_test(n, k=100):
+    if n <= 1:
+        return False
+    for i in range(k):
+        a = randint(1, n - 1)
+        if pow(a, n - 1, n) != 1:
+            return False
+    return True
+
+```
+
+``` python
+fermat_test(0)  # False
+fermat_test(1)  # False
+fermat_test(561)  # False
+fermat_test(41041)  # False
+fermat_test(17)  # True
+fermat_test(162259276829213363391578010288127)  # True
+fermat_test(-1)  # False
+```