feat(pref sums): add p50 - #54

• Add Euler p50 solver to find longest consecutive-prime sum below a limit.
• Use sieve-generated primality table plus prime prefix sums for fast range-sum checks.
• Add pytest coverage asserting the known 1,000,000-limit result.

graph TD
  T["tests/euler/p50_test.py"] --> F["consecutive_prime_sum()"] --> R["Longest prime"]
  M["Algorithms/.../p50.py"] --> F --> P["Prefix sums"] --> C["Scan ranges"]
  M --> S["sieve()"] --> L["Prime table"]

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The following are alternative approaches to this PR:

1. Extract shared prime utilities module

• ➕ Removes duplicated is_prime/sieve logic across Euler solutions
• ➕ Centralizes correctness/performance fixes and test coverage
• ➖ Adds an extra abstraction layer for what are currently stand-alone puzzle solutions
• ➖ Requires updating imports across multiple existing files

2. Use a two-pointer/sliding-window over prefix sums

• ➕ Can reduce search space vs nested loops by exploiting monotonicity of sums
• ➕ Often faster for larger limits while preserving the prefix-sum approach
• ➖ More complex control flow and harder to reason about correctness
• ➖ Less straightforward to keep the “longest length” invariant correct

3. Leverage an external number theory library (e.g., sympy)

• ➕ Battle-tested primality and prime generation
• ➕ Potentially simpler code
• ➖ Introduces a heavy new dependency for a small utility repo
• ➖ May conflict with repository goals around minimal dependencies/learning implementations

Recommendation: The current sieve + prefix-sums approach is the right baseline for Euler p50 (simple, fast enough at 1e6, easy to test). If this repo continues adding many prime-based Euler problems, the most valuable follow-up is extracting shared prime utilities to avoid repeated implementations and to centralize performance/correctness improvements.

Enhancement (1) +45 / -0

p50.pyImplement Euler p50 solver with sieve + prime prefix sums +45/-0

Implement Euler p50 solver with sieve + prime prefix sums

• Adds primality helpers (trial-division is_prime and sieve) and implements consecutive_prime_sum(n) using a prime list plus prefix sums to check all candidate consecutive-prime ranges under n while tracking the longest valid prime sum.

Algorithms/numerical_methods/euler/p50.py

Tests (1) +4 / -0

p50_test.pyAdd regression test for Euler p50 known 1e6 result +4/-0

Add regression test for Euler p50 known 1e6 result

• Introduces a pytest that asserts consecutive_prime_sum(1_000_000) returns the known Project Euler answer (997651).

tests/euler/p50_test.py

Description

Algorithms.numerical_methods.euler.p50.is_prime uses math.sqrt without importing math, so calling
is_prime will raise NameError at runtime.

Code

Algorithms/numerical_methods/euler/p50.py[R1-16]

+from typing import Optional
+
+def is_prime(n: int):
+    if n < 1:
+        raise ValueError("n must be at least 1")
+    elif n == 1:
+        return False
+    elif n == 2:
+        return True
+    elif n % 2 == 0:
+        return False
+    else:
+        for i in range(3, int(math.sqrt(n))+1):
+            if n % i == 0:
+                return False
+        return True

Relevance

⭐⭐⭐ High

PR #53’s similar is_prime uses math.sqrt and explicitly imports math; team likely fixes missing
imports.

PR-#53

ⓘ Recommendations generated based on similar findings in past PRs

Evidence

In p50.py, math.sqrt is referenced inside is_prime() but there is no import math in the module
imports. In p49.py, the same pattern includes import math, showing the missing import in p50.py is
not intentional.

Algorithms/numerical_methods/euler/p50.py[1-16]
Algorithms/numerical_methods/euler/p49.py[1-18]

Agent prompt

The issue below was found during a code review. Follow the provided context and guidance below and implement a solution

### Issue description
`Algorithms/numerical_methods/euler/p50.py` defines `is_prime()` that calls `math.sqrt(...)` but the module never imports `math`, causing a `NameError` when `is_prime()` is executed.

### Issue Context
A similar `is_prime()` implementation in `p49.py` imports `math` at module scope.

### Fix Focus Areas
- Algorithms/numerical_methods/euler/p50.py[1-16]

ⓘ Copy this prompt and use it to remediate the issue with your preferred AI generation tools

Description

sieve() initializes the returned primality array to all True and never sets indices 0 and 1 to
False, so the returned lookup table incorrectly reports 0 and 1 as prime.

Code

Algorithms/numerical_methods/euler/p50.py[R18-26]

+def sieve(n: int):
+    is_prime = [True]*(n+1)
+    primes = []
+    for p in range(2, n+1):
+        if is_prime[p]:
+            primes.append(p)
+            for v in range(p*p, n+1, p):
+                is_prime[v] = False
+    return is_prime, primes

Relevance

⭐⭐ Medium

No repo history found about sieve() needing is_prime[0]=is_prime[1]=False; enforcement unclear.

ⓘ Recommendations generated based on similar findings in past PRs

Evidence

p50.py returns the boolean array directly without ever correcting 0/1. Another sieve implementation
in the repo explicitly sets indices 0 and 1 to False, demonstrating the expected invariant for such
tables.

Algorithms/numerical_methods/euler/p50.py[18-26]
dataSecurity/RSAEncryption/primality.py[8-19]

Agent prompt

The issue below was found during a code review. Follow the provided context and guidance below and implement a solution

### Issue description
`sieve(n)` returns a boolean primality table but leaves `is_prime[0]` and `is_prime[1]` as `True`, which is incorrect and can break any caller that relies on the returned table.

### Issue Context
There is an existing sieve implementation in the repo that explicitly sets 0 and 1 to non-prime.

### Fix Focus Areas
- Algorithms/numerical_methods/euler/p50.py[18-26]

ⓘ Copy this prompt and use it to remediate the issue with your preferred AI generation tools

Description

tests/euler/p50_test.py is missing a trailing newline at end-of-file, which creates unnecessary diff
noise and may trip formatting/lint checks.

Code

tests/euler/p50_test.py[R1-4]

+from Algorithms.numerical_methods.euler.p50 import consecutive_prime_sum
+
+def test_sol():
+    assert consecutive_prime_sum(n=1_000_000) == 997651

Relevance

⭐⭐⭐ High

Trailing EOF newline was previously accepted as a cleanup fix (PR #49).

PR-#49

ⓘ Recommendations generated based on similar findings in past PRs

Evidence

The added test file content ends at line 4 (no trailing newline). A similar missing-newline issue
was previously accepted as a fix in this repo, indicating this is a recurring style/maintenance
concern.

tests/euler/p50_test.py[1-4]
PR-#49

Agent prompt

The issue below was found during a code review. Follow the provided context and guidance below and implement a solution

### Issue description
The test file does not end with a newline character.

### Issue Context
This repo has previously accepted fixes to add trailing newlines to avoid repeated diffs on unchanged lines.

### Fix Focus Areas
- tests/euler/p50_test.py[1-4]

ⓘ Copy this prompt and use it to remediate the issue with your preferred AI generation tools