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Products that do what Goldbach Conjecture up to 4*10^18+7*10^13 does
Achieved a new world record in verifying the Goldbach Conjecture using grid computing, by extending the verification up to 4 quadrillion (4×10¹⁸) + 70 trillion (7×10¹³). My grid computing system - Gridbach is a cloud-based distributed computing system accessible from any PC or smartphone. It requires no login or app installation. The high-performance WASM (WebAssembly) binary code is downloaded as browser content, enabling computation on the user’s browser. [Website] https://gridbach.com/ [Medium]…
- 1SA
I made a chess engine today, and made it fit within 2KB. I used a variant of MinMax called Negamax, with alpha beta pruning. For the board representation I have used a 120-cell "mailbox". I managed to squeeze in checkmate/stalemate in there, after trimming out some edge cases. I am a great fan of demoscene (computer art subculture) since middle school, and hence it was a ritual i had to perform. For estimating the Elo, I measured 240 automated games against Stockfish Elo levels (1320 to 1600) under fixed depth-5 and some constrained rules, using equal color distribution. Then converted…
Feb 2026 · github.com
- 2ZC
Zero-Knowledge Proofs (ZKPs) let an untrusted proved show that computation was executed correctly without revealing the inputs to the verifier. However to prove anything, the computation first has to be expressed as a circuit: a system of polynomial equations (constraints) over a finite field. Circuits are the assembly language of zk and every constraint costs prover (and sometimes verifier) time, so production circuits are aggressively hand-optimized. Over the last months, we have been experimenting with writing formal specifications instead and letting LLMs produce the circuits: as long as…
Jul 2026 · zk.golf
- 3CF
Oct 2025 · github.com
- 4FV
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. The experience of working with AI agents on this project changed a lot with recent model releases, as I describe in the readme. Opus 4.8 is able to provide algorithm implementation with formal proof in one shot, whereas previous models required me to provide proof strategies in multiple steps. Trust in the correctness comes entirely from the Lean checker and human review of a small specification, not from the LLM. Also check out the web demo built around the verified core linked in…
Jun 2026 · github.com
- 5FV
To my knowledge, this is the first formally verified implementation of a 3D constructive solid geometry (CSG) operation: mesh intersection, implemented in Lean 4 and verified against a concise specification that pins down the surface of the resulting mesh exactly and guarantees practical well-formedness conditions on the triangulation. This project is also an experiment in avoiding having to trust AI-generated code. A human reviewer only needs to read 93 lines of formal specification and run the Lean checker to certify the correctness of the kernel, skipping the intricate 1000+ lines of…
Jul 2026 · github.com
- 6AN
The core question: how did HP's scientific calculators actually work at the gate level? That rabbit hole led to building one from scratch. The architectural decision everything else follows from: a decimal calculator should store numbers as BCD — one decimal digit per 4-bit nibble. A standard byte-oriented CPU (Z80, 6502) fights that layout constantly. So I designed a small custom CPU in Verilog where 4 bits is the natural data width and memory is nibble addressable. What the project covers: - Custom CPU: Harvard architecture, 12-bit ISA, 8-state execution FSM, hardware stack guard with a…
May 2026 · github.com
- 7BA
2020 · andrewsun.com
- 8AM
2012 · github.com
- 9AG
This is a vector index I built that supports insertion and k-nearest neighbors (k-NN) querying, optimized for GPUs. It operates entirely in CUDA and can process queries on half a billion vectors in under 200 milliseconds. The codebase is structured as a standalone library with an HTTP API for remote access. It’s intended for high-performance search tasks—think similarity search, AI model retrieval, or reinforcement learning replay buffers. The codebase is located at https://github.com/rodlaf/BinaryGPUIndex.
2025 · rlafuente.com
- 10
- 11TK
I analyzed two orderings of the 64 I Ching hexagrams and found the permutation cycle decomposition between them is [52, 10, 2] with zero fixed points. Nobody has done this kind of analysis before and this cycle type has not been reported in the literature. You can verify it yourself.
Mar 2026 · gzw1987-bit.github.io
- 12SS
We were genuinely impressed by Yann LeCun’s recent announcement about his Sudoku solver based on Energy-Based Models here: https://logicalintelligence.com/yann-lecun So we (a software engineer and prodigy mathematician) worked in the weekend to see if we can beat it and we did! If Kona solves puzzles in 313 milliseconds, we currently solve 270,000 puzzles per second! We do not know the internal mechanics behind Logical Intelligence’s system, but we are happy to share ours in the webpage there is a full description, code and also a paper published. Why people are obsessed with…
Feb 2026 · davisgeometric.com
- 13CP
Here is the protocol worklow. Let us define g as the generator of the multiplicative cyclic group G of order q. Let us define p = 2q + 1 (a safe prime). The values p, g, a1, b1, c1 are publicly available to the prover and the verifier. a1 = g^a mod q b1 = g^b mod q c1 = g^ab mod q where a and b are cryptographically secure randomly generated numbers. prover wants to prove he knows a secret x. the prover computes y1 = g^x mod q and y2 = b1^x mod q. the prover sends y1 and y2 to the verifier. The verifier then computes a challenge value s and sends it to the prover. the prover then computes z…
2025 · github.com
- 14IB
I've always been fascinated by cryptographic principles, so I decided to dive deep into zero-knowledge proofs and implement a Groth16 proof verifier entirely in Rust. This project validates cryptographic proofs and demonstrates how succinct, verifiable computations can be achieved. Using Rust's powerful libraries like arkworks, I implemented pairing checks, public input commitments, and proof validation logic while ensuring the code remains modular and efficient. I handled the complexities of affine group operations, scalar multiplications, and optimized public input verification to make…
2024 · github.com
- 15TT
2017 · npmjs.com
- 16HA
Most ZK proving systems are optimized for server-grade hardware with massive RAM. When scaling to industrial-sized traces (2^20+ rows), they often hit a "Memory Wall" where allocation and data movement become a larger bottleneck than the actual computation. I have been developing Hekate, a ZK engine written in Rust that utilizes a Zero-Copy streaming model and a hybrid tiled evaluator. To test its limits, I ran a head-to-head benchmark against Binius64 on an Apple M3 Max laptop using Keccak-256. The results highlight a significant architectural divergence: At 2^15 rows: Binius64 is faster…
Jan 2026
- 17SA
Hey HN, I’m a physicist turned quant. Some friends and I 'built' SymDerive because we wanted a symbolic math library that was "Agent-Native" by design, but still a practical tool for humans. It boils down to two main goals: 1. Agent Reliability: I’ve found that AI agents write much more reliable code when they stick to stateless, functional pipelines (Lisp-style). It keeps them from hallucinating state changes or getting lost in long procedural scripts. I wanted a library that enforces that "Input -> Transform -> Output" flow by default. 2. Easing the transition to Python: For many…
Feb 2026
- 18
A new programming language rooted in Pure Mathematics
2025
- 19ZP
The model uses a 1024-dimensional complex Hilbert space with 32 layers of programmable Mach–Zehnder meshes (Reck architecture) and derives token probabilities directly via the Born rule. Despite using only unitary operations and no attention mechanism, a 1024×32 model achieves coherent TinyStories generation after < 1.8 hours of training on a single consumer GPU. This is Part 1 - the next step is physical implementation with $50 of optics from AliExpress.
Nov 2025 · zenodo.org
- 20DB
The only way to get a trust-less random value is to have it distributed and time-locked three ways, player, server and a future-entropy. In the demo above, the moment you commit (Roll-Dice) a commit with the hash of a player secret is sent to the server and the server accepts that and sends back the hash of its secret back and the "future" drand round number at which the randomness will resolve. The future used in the demo is 10 secs When the reveal happens (after drand's particular round) all the secrets are revealed and the random number is generated using…
Feb 2026 · blockrand.net
- 21OS
We’ve just released an open-source library for solving the Maximum Independent Set (MIS) problem with neutral atom quantum computing, running on both quantum processing units (QPUs) and classical hardware, thanks to emulators. This project is the result of collaboration between Pasqal, academic researchers, and industry partners, aiming to make it practical to experiment with quantum approaches to hard combinatorial optimization tasks. The MIS problem appears in real-world scenarios like scheduling, resource allocation, and network optimization, areas where classical solvers often struggle…
2025
- 22RR
runNburn is an Apache-2.0 Rust inference engine for quantized GGUF models that are too big for your fast memory. The core idea: weights stay file-backed (mmap), host residency stays under an explicit byte budget (--ram-budget), and GPU caches are sized from detected free/total VRAM — never from device-name presets. There is no conversion step, no sidecar cache files, no silent requantization. The GGUF on disk is the single source of truth. The result that made me want to post this: Tencent's Hy3 (295B total / 21B active sparse MoE, a single 97.8 GiB Q2_K GGUF) runs on my desktop…
Jul 2026 · github.com
- 23TT
Hi HN, I am one of the cofounders of http://turingdb.ai. We built TuringDB while working on large biological knowledge graphs and graph-based digital twins with pharma & hospitals, where existing graph databases were unusable for deep graph traversals with hundreds or thousands of hops on (crappy) machines you can find in a hospital. https://github.com/turing-db/turingdb TuringDB is a new in-memory, column-oriented graph database optimised for read-heavy analytical workloads: - Milliseconds (1) for multi-hop queries on graphs with 10M+ nodes/edges -…
Jan 2026 · github.com
- 24SA
Hi everyone, I’m a student with a strong interest in computer science and complexity theory. Recently, I worked on a manuscript attempting to prove that P ≠ NP. I know how this sounds — it’s one of the hardest and most debated problems in CS, and many have tried and failed. I don’t claim to have the final answer, but I believe the approach I used might at least offer some fresh perspective or provoke useful critique. The idea involves geometric separation between deterministic and nondeterministic computation, using high-dimensional lattice constructions and some physics-inspired intuition.…
2025 · zenodo.org
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