lookprime

lookprime is a high-performance prime number library for Python built around a memory-mapped, odd-only, bitset sieve.

It is designed for: - extremely fast primality tests - fast prime counting and enumeration - repeated queries across processes - large limits with minimal RAM overhead - CLI benchmarking and inspection

The core idea:
👉 build a prime sieve once, store it on disk, then reuse it via mmap with near-zero startup cost.

Features

Core performance

• Odd-only sieve (½ the memory of full sieve)
• Bitset representation (1 bit per odd number)
• Memory-mapped cache (mmap) for zero-copy sharing
• int.from_bytes(...).bit_count() for fast counting
• Auto-growing cache when needed
• Safe for multi-process use (read-only)

Python API

• isprime(n)
• isprime_many(iterable)
• primerange(a, b)
• randprime(a, b)
• primepi(n)
• prime(n) (nth prime, 1-indexed)
• prevprime(n)
• nextprime(n)
• primes(n) (first n primes)
• primes_up_to(n)
• factorint(n)
• cache_info()
• clear_cache()

CLI

• lookprime info
• lookprime build
• lookprime benchmark
• lookprime isprime <n>
• lookprime factor <n>
• lookprime clear-cache

Installation

pip install lookprime

Python ≥ 3.9 required.

Quick Start (Python)

import lookprime

lookprime.isprime(97)                 # True
lookprime.primepi(1_000_000)          # 78498
lookprime.primes_up_to(50)            # [2, 3, 5, 7, 11, ...]
lookprime.factorint(123456)           # {2: 6, 3: 1, 643: 1}

Bulk checks:

lookprime.isprime_many([2, 3, 4, 5, 10**9 + 7])

How the Cache Works

• Sieve files are stored in a platform-appropriate cache directory:

  • Linux: ~/.cache/lookprime
  • macOS: ~/Library/Caches/lookprime
  • Windows: %LOCALAPPDATA%\lookprime\Cache

• Each sieve is stored as:

  lookprime_mask_<limit>.lpm
  

• Files are memory-mapped (mmap) and shared across processes

• Rebuilding happens only if needed

To inspect cache state:

lookprime.cache_info()

To delete all cached sieves:

lookprime.clear_cache()

or from CLI:

lookprime clear-cache

CLI Usage

Show system and cache info

lookprime info

Build a sieve explicitly

lookprime build --limit 100000000

Benchmark lookup speed

lookprime benchmark

Options:

lookprime benchmark \
  --limit 100000000 \
  --duration 1.0 \
  --iterations 25 \
  --chunk 65536

Environment override:

export LOOKPRIME_CHUNK=65536
lookprime benchmark

Primality from CLI

lookprime isprime 104729

Factor integers from CLI

lookprime factor 123456

Performance Notes

• isprime(n) is O(1) after cache load
• primepi(n) uses bitset population count
• prime(n) and primes(n) use fast bit scanning
• Cache memory is shared between processes
• No Python objects are created per lookup

Threading & Multiprocessing

• The sieve is read-only
• Safe to open in multiple processes
• Each process memory-maps its own view
• No locks required

License

MIT License.