From 207331ae6dd0908f46e0355d32d9ae2d122fc775 Mon Sep 17 00:00:00 2001
From: Freddy Pringle <freddyjepringle@gmail.com>
Date: Fri, 9 Oct 2020 21:40:35 +0200
Subject: [PATCH 1/2] Added solution for Project Euler problem 87. Fixes: #2695

---
 project_euler/problem_87/__init__.py |  0
 project_euler/problem_87/sol1.py     | 50 ++++++++++++++++++++++++++++
 2 files changed, 50 insertions(+)
 create mode 100644 project_euler/problem_87/__init__.py
 create mode 100644 project_euler/problem_87/sol1.py

diff --git a/project_euler/problem_87/__init__.py b/project_euler/problem_87/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/project_euler/problem_87/sol1.py b/project_euler/problem_87/sol1.py
new file mode 100644
index 000000000000..dc42f8a46bda
--- /dev/null
+++ b/project_euler/problem_87/sol1.py
@@ -0,0 +1,50 @@
+"""
+The smallest number expressible as the sum of a prime square, prime cube, and prime
+fourth power is 28. In fact, there are exactly four numbers below fifty that can be
+expressed in such a way:
+
+28 = 22 + 23 + 24
+33 = 32 + 23 + 24
+49 = 52 + 23 + 24
+47 = 22 + 33 + 24
+
+How many numbers below fifty million can be expressed as the sum of a prime square,
+prime cube, and prime fourth power?
+"""
+
+
+def solution(limit: int = 50000000) -> int:
+    """
+    Return the number of integers less than limit which can be expressed as the sum
+    of a prime square, prime cube, and prime fourth power.
+    >>> solution(50)
+    4
+    """
+    ret = set()
+    prime_square_limit = int((limit - 24) ** (1 / 2))
+
+    primes = set(range(3, prime_square_limit + 1, 2))
+    primes.add(2)
+    for p in range(3, prime_square_limit + 1, 2):
+        if p not in primes:
+            continue
+        primes.difference_update(set(range(p * p, prime_square_limit + 1, p)))
+
+    for prime1 in primes:
+        square = prime1 * prime1
+        for prime2 in primes:
+            cube = prime2 * prime2 * prime2
+            if square + cube >= limit - 16:
+                break
+            for prime3 in primes:
+                tetr = prime3 * prime3 * prime3 * prime3
+                total = square + cube + tetr
+                if total >= limit:
+                    break
+                ret.add(total)
+
+    return len(ret)
+
+
+if __name__ == "__main__":
+    print(solution())

From 07afdeaf0f5bdf0c5ca0f0f3c597beb6e71a3f88 Mon Sep 17 00:00:00 2001
From: Freddy Pringle <freddyjepringle@gmail.com>
Date: Thu, 15 Oct 2020 11:02:25 +0200
Subject: [PATCH 2/2] Update docstring and 0-padding in directory name.
 Reference: #3256

---
 project_euler/{problem_87 => problem_087}/__init__.py | 0
 project_euler/{problem_87 => problem_087}/sol1.py     | 4 +++-
 2 files changed, 3 insertions(+), 1 deletion(-)
 rename project_euler/{problem_87 => problem_087}/__init__.py (100%)
 rename project_euler/{problem_87 => problem_087}/sol1.py (93%)

diff --git a/project_euler/problem_87/__init__.py b/project_euler/problem_087/__init__.py
similarity index 100%
rename from project_euler/problem_87/__init__.py
rename to project_euler/problem_087/__init__.py
diff --git a/project_euler/problem_87/sol1.py b/project_euler/problem_087/sol1.py
similarity index 93%
rename from project_euler/problem_87/sol1.py
rename to project_euler/problem_087/sol1.py
index dc42f8a46bda..f444481c17ac 100644
--- a/project_euler/problem_87/sol1.py
+++ b/project_euler/problem_087/sol1.py
@@ -1,4 +1,6 @@
 """
+Project Euler Problem 87: https://projecteuler.net/problem=87
+
 The smallest number expressible as the sum of a prime square, prime cube, and prime
 fourth power is 28. In fact, there are exactly four numbers below fifty that can be
 expressed in such a way:
@@ -47,4 +49,4 @@ def solution(limit: int = 50000000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution())
+    print(f"{solution() = }")