From 74ac4927d7caad179c398b7bb8a54c71e783ef2e Mon Sep 17 00:00:00 2001
From: Charles Cabergs <me@cacharle.xyz>
Date: Thu, 14 Jan 2021 17:04:16 +0100
Subject: problem 46 in python

---
 python/046-goldbachs_other_conjecture.py | 54 ++++++++++++++++++++++++++++++++
 1 file changed, 54 insertions(+)
 create mode 100644 python/046-goldbachs_other_conjecture.py

(limited to 'python/046-goldbachs_other_conjecture.py')

diff --git a/python/046-goldbachs_other_conjecture.py b/python/046-goldbachs_other_conjecture.py
new file mode 100644
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--- /dev/null
+++ b/python/046-goldbachs_other_conjecture.py
@@ -0,0 +1,54 @@
+###
+# Goldbach's other conjecture
+# Problem 46
+#
+# It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
+# 9 = 7 + 2×1^2
+# 15 = 7 + 2×2^2
+# 21 = 3 + 2×3^2
+# 25 = 7 + 2×3^2
+# 27 = 19 + 2×2^2
+# 33 = 31 + 2×1^2
+# It turns out that the conjecture was false.
+# What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
+###
+
+
+import itertools
+import math
+
+
+def is_prime(n):
+    if n == 0 or n == 1:
+        return False
+    if n == 2 or n == 3 or n == 5 or n == 7:
+        return True
+    if n % 2 == 0 or n % 3 == 0:
+        return False
+    for d in range(6, math.ceil(math.sqrt(n)) + 2, 6):
+        if n % (d - 1) == 0 or n % (d + 1) == 0:
+            return False
+    return True
+
+
+for n in itertools.count(3, 2):
+    if is_prime(n):
+        continue
+    found = False
+    s = 0
+    for x in itertools.count(1):
+        s = 2 * (x * x)
+        # print(n, s)
+        # print(s)
+        if s >= n:
+            # if not found:
+            #     print(">>>", n)
+            break
+        if is_prime(n - s):
+            # print(n, math.sqrt(s / 2), n - s)
+            found = True
+            break
+    if not found:
+        print(n, math.sqrt(s / 2), n -s)
+        break
+
-- 
cgit