From 66eeb6d117192755d13e84984419a0d8e4ffb728 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Mon, 5 Oct 2026 05:54:22 -0400
Subject: [PATCH] Solve problem 214

---
 python/e214.py | 51 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 python/e214.py

diff --git a/python/e214.py b/python/e214.py
new file mode 100644
index 0000000..2a0b80f
--- /dev/null
+++ b/python/e214.py
@@ -0,0 +1,51 @@
+from lib_prime import primes
+from functools import cache
+from math import gcd
+
+
+def get_phi_table(n: int, ps: list[int]) -> list[int]:
+    tbl = [-1] * (n + 2)
+    tbl[1] = 1
+    queue = [(1, 1, 0)]
+
+    while queue:
+        x, phi, pi = queue.pop()
+        for pin in range(pi, len(ps)):
+            p = ps[pin]
+            tbl[p] = p - 1
+            xn = x * p
+            if xn > n:
+                break
+            d = gcd(x, p)
+            phid = tbl[d]
+            assert phid != -1
+            phin = (phi * (p - 1) * d) // phid
+            tbl[xn] = phin
+            queue.append((xn, phin, pin))
+    return tbl
+
+
+def euler_214():
+    n = 40 * 10**6
+    ps = primes(n)
+    tbl = get_phi_table(n, ps)
+
+    @cache
+    def chain(n: int) -> int:
+        if n == 1:
+            return 1
+        n = tbl[n]
+        return 1 + chain(n)
+
+    s = 0
+    for i in range(len(ps)):
+        p = ps[i]
+        if chain(p) == 25:
+            s += p
+    return s
+
+
+if __name__ == "__main__":
+    solution = euler_214()
+    print(f"e214.py: {solution}")
+    assert solution == 1677366278943