From f588a2e670f9cd92590ee535619168ca933b8098 Mon Sep 17 00:00:00 2001
From: Charles Cabergs <me@cacharle.xyz>
Date: Thu, 14 Jan 2021 14:30:56 +0100
Subject: problem 47 in python

---
 python/047-distinct_primes_factors.py | 49 +++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 python/047-distinct_primes_factors.py

(limited to 'python/047-distinct_primes_factors.py')

diff --git a/python/047-distinct_primes_factors.py b/python/047-distinct_primes_factors.py
new file mode 100644
index 0000000..30b76bc
--- /dev/null
+++ b/python/047-distinct_primes_factors.py
@@ -0,0 +1,49 @@
+###
+# Distinct primes factors
+# Problem 47
+#
+# The first two consecutive numbers to have two distinct prime factors are:
+#
+# 14 = 2 × 7
+# 15 = 3 × 5
+#
+# The first three consecutive numbers to have three distinct prime factors are:
+#
+# 644 = 2² × 7 × 23
+# 645 = 3 × 5 × 43
+# 646 = 2 × 17 × 19.
+#
+# Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
+###
+
+
+import itertools
+
+
+# from: https://en.wikipedia.org/wiki/Trial_division
+def count_prime_factors(num):
+    factors = []
+    if num % 2 == 0:
+        factors.append(2)
+    while num % 2 == 0:
+        num //= 2
+    f = 3
+    while f * f <= num:
+        if num % f == 0:
+            if not f in factors:
+                factors.append(f)
+            num //= f
+        else:
+            f += 2
+    if num != 1:
+        factors.append(num)
+    return len(factors)
+
+
+for n in itertools.count(1):
+    if (count_prime_factors(n) == 4 and
+        count_prime_factors(n + 1) == 4 and
+        count_prime_factors(n + 2) == 4 and
+        count_prime_factors(n + 3) == 4):
+            print(n)
+            break
-- 
cgit