Executive summary
k-tuplet-search adapts a staged GPU/CPU search architecture to additive prime patterns. It contains a 97-pattern CUDA catalog for tuple lengths 3 through 28, wheel construction, GPU residue filtering, GMP confirmation, checkpointed campaign operation, a sourced known-record corpus, and an interactive analyzer. The repository can reproduce known examples and run long search cells, but it does not claim a new k-tuplet record. That distinction makes the work useful as an engine and reproducibility artifact rather than a results announcement.
Problem and context
A prime k-tuplet asks whether every value in an admissible offset pattern is prime at the same base. At large sizes, most candidates must be rejected with cheap residue tests before probable-prime confirmation. The project ports the filtering style developed for Cunningham chains while changing the candidate formula and pattern machinery.
What was built
- A generated C catalog of 97 admissible narrow-diameter patterns.
- Plain and quotient-style primorial wheel expressions.
- A staged CUDA filter with prefix lanes, random and sequential modes,
- CPU GMP confirmation and a separate GPU oracle engine.
- PARI/GP planning tools and self-tests.
- A sourced JSON corpus and generation scripts for known-record replay.
- Campaign, benchmark, migration, and command-reference documentation.
checkpoint/resume, and JSONL hit persistence.
How it works
The wheel selects base positions that survive small-prime constraints. GPU stages then apply progressively more expensive forbidden-residue and Fermat filters. The small survivor set moves to the host for GMP/BPSW verification of every member of the pattern.
Operational controls divide the prefix space, persist progress, and cap campaign cells. Quotient wheel expressions allow selected small primes to remain outside the initial wheel when comparing filter tradeoffs.
Evidence and validation
The May 2026 release snapshot records 52 passing CUDA-engine tests on the stated RTX 5090 and CUDA 13.2 configuration. Known-record gates draw from 227 sourced records across k=16..21, while the PARI/GP library runs 39 self-tests. Longevity runs are labeled as stability and sampling evidence rather than exhaustive coverage.
Boundaries
No new record is claimed. The local pattern-generation tools are conveniences; the repository names Norman Luhn's maintained pattern and Hardy–Littlewood tables as the mathematical reference. Searches above the maintained record range are exploratory. Default CUDA paths and architecture flags must be changed for hardware other than the documented Blackwell setup.
Repository map and first run
cd src/cuda
make kt_filter_v8 NVCC=/path/to/nvcc NVCC_ARCH=sm_89
./kt_filter_v8 --test
./kt_filter_v8 --list-patternsUse docs/CUDA_CLI_REFERENCE.md for the full interface, TESTING.md for gates and benchmark interpretation, known/records.json for the record corpus, and visualizations/ for the live analyzer.