A Lock-Free, Fully GPU-Resident Architecture for the Verification of Goldbach's Conjecture
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908873037709312 |
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| author | Llorente-Saguer, Isaac |
| author_facet | Llorente-Saguer, Isaac |
| contents | We present a fully device-resident, multi-GPU architecture for the large-scale computational verification of Goldbach's conjecture. In prior work, a segmented double-sieve eliminated monolithic VRAM bottlenecks but remained constrained by host-side sieve construction and PCIe transfer latency. In this work, we migrate the entire segment generation pipeline to the GPU using highly optimised L1 shared-memory tiling, achieving near-zero host-device communication during the critical verification path. To fully leverage heterogeneous multi-GPU clusters, we introduce an asynchronous, lock-free work-stealing pool that replaces static workload partitioning with atomic segment claiming, enabling $99.7$% parallel efficiency at 2 GPUs and $98.6$% at $4$ GPUs. We further implement strict mathematical overflow guards guaranteeing the soundness of the 64-bit verification pipeline up to its theoretical ceiling of $1.84 \times 10^{19}$. On the same hardware, the new architecture achieves a $45.6\times$ algorithmic speedup over its host-coupled predecessor at N = $10^{10}$. End-to-end, the framework verifies Goldbach's conjecture up to $10^{12}$ in $36.5$ seconds on a single NVIDIA RTX 5090, and up to $10^{13}$ in $133.5$ seconds on a four-GPU system. All code is open-source and reproducible on commodity hardware. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Lock-Free, Fully GPU-Resident Architecture for the Verification of Goldbach's Conjecture Llorente-Saguer, Isaac Mathematical Software Distributed, Parallel, and Cluster Computing Performance Number Theory 11Y16 (Primary), 11P32, 68W10 D.1.3; F.2.1 We present a fully device-resident, multi-GPU architecture for the large-scale computational verification of Goldbach's conjecture. In prior work, a segmented double-sieve eliminated monolithic VRAM bottlenecks but remained constrained by host-side sieve construction and PCIe transfer latency. In this work, we migrate the entire segment generation pipeline to the GPU using highly optimised L1 shared-memory tiling, achieving near-zero host-device communication during the critical verification path. To fully leverage heterogeneous multi-GPU clusters, we introduce an asynchronous, lock-free work-stealing pool that replaces static workload partitioning with atomic segment claiming, enabling $99.7$% parallel efficiency at 2 GPUs and $98.6$% at $4$ GPUs. We further implement strict mathematical overflow guards guaranteeing the soundness of the 64-bit verification pipeline up to its theoretical ceiling of $1.84 \times 10^{19}$. On the same hardware, the new architecture achieves a $45.6\times$ algorithmic speedup over its host-coupled predecessor at N = $10^{10}$. End-to-end, the framework verifies Goldbach's conjecture up to $10^{12}$ in $36.5$ seconds on a single NVIDIA RTX 5090, and up to $10^{13}$ in $133.5$ seconds on a four-GPU system. All code is open-source and reproducible on commodity hardware. |
| title | A Lock-Free, Fully GPU-Resident Architecture for the Verification of Goldbach's Conjecture |
| topic | Mathematical Software Distributed, Parallel, and Cluster Computing Performance Number Theory 11Y16 (Primary), 11P32, 68W10 D.1.3; F.2.1 |
| url | https://arxiv.org/abs/2603.07850 |