From 0e82dac7ca8afa5453a10f452cd0e9753657b1e2 Mon Sep 17 00:00:00 2001
From: felixm <mail@felixm.de>
Date: Sun, 21 Apr 2024 10:11:40 -0400
Subject: [PATCH] Solve problem 357.

---
 python/e357.py | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 python/e357.py

diff --git a/python/e357.py b/python/e357.py
new file mode 100644
index 0000000..0dfe6c5
--- /dev/null
+++ b/python/e357.py
@@ -0,0 +1,41 @@
+def primes_sieve(nmax):
+    a = [0 for _ in range(nmax)]
+    for i in range(2, nmax):
+        if a[i] == 0:
+            for j in range(i + i, nmax, i):
+                a[j] = i
+    return a
+
+
+def is_number(n, primes):
+    f = n // 2
+    if primes[f] == 0:
+        for d in [2, f]:
+            if primes[d + n // d] != 0:
+                return False
+        return True
+
+    for d in range(1, n // 2 + 1):
+        if n % d == 0:
+            if primes[d + n // d] != 0:
+                return False
+        if d * d > n:
+            break
+    return True
+
+
+def euler_357():
+    r = 1 # n = 1 is a number
+    ps = primes_sieve(100_000_000)
+    for p in range(3, len(ps)):
+        if ps[p] == 0:
+            n = p - 1
+            if is_number(n, ps):
+                r += n
+    return r
+
+
+if __name__ == "__main__":
+    solution = euler_357()
+    print("e357.py: " + str(solution))
+    assert solution == 1739023853137