🚀 Just broke the 1 Tera-item/s barrier! 🚀

turkishsieve — Fri, 30 Jan 2026 12:51:16 +0000

Using the new RTX 5090, my "Turkish Sieve Engine" reached 1.136 Trillion items/s in prime gap analysis.

🔹 Range 10^12: 0.880s
🔹 Range 10^14: 359s
🔹 Methodology: N/6 Bit-Indexing

Scientific record archived at Zenodo [https://doi.org/10.5281/zenodo.18038661] 🧵👇
GitHub: [https://github.com/bilgisofttr/turkishsieve]

#HPC #CUDA #Math #RTX5090 #PrimeNumbers

The Turkish Sieve Methodology: Deterministic Computation of Twin and Cousin Prime Pairs Using an N/6 Bit Data Structure

turkishsieve — Mon, 19 Jan 2026 12:07:22 +0000

https://github.com/bilgisofttr/turkishsieve

A CPU&GPU-Accelerated Prime Number Generator" description: "N/6 Bit methodology for efficient twin and cousin prime enumeration. https://github.com/bilgisofttr/turkishsieve

turkishsieve — Sun, 18 Jan 2026 08:58:39 +0000

GitHub - bilgisofttr/turkishsieve: The Turkish Sieve Methodology: Deterministic Computation of Twin and Cousin Prime Pairs Using an N/6 Bit Data Structure

The Turkish Sieve Methodology: Deterministic Computation of Twin and Cousin Prime Pairs Using an N/6 Bit Data Structure - bilgisofttr/turkishsieve

github.com

Turkish Sieve Engine (TSE) V.1.0.0

turkishsieve — Sun, 18 Jan 2026 05:09:03 +0000

🚀 Turkish Sieve Engine (TSE) V.1.0.0

Unique, Compact & Massive-Parallel Prime Discovery Engine

📌 Introduction

Turkish Sieve Engine (TSE) is a revolutionary application that combines unprecedented computational efficiency, compact memory structures, and massive parallelization in prime number research. Based on the scientific methodology published on Zenodo (DOI: 10.5281/zenodo.18038661), TSE is the most efficient academic tool designed for the detection of primes, twin primes, and cousin primes within any given range, including massive scales ($10^{14}$ and beyond).

📊 Key Metrics & Achievements

Peak Throughput: 181.5 Billion candidates/sec (measured on RTX 3070 @ $10^{12}$ range).
Memory Efficiency: N/6 bit data structure (6x more compact than classical sieves).
GPU Acceleration: Up to 11.0× speedup compared to multi-core CPUs in optimal ranges.
Scientific Accuracy: 100% compliance with OEIS A007508 (Zero error margin for twin primes).
First Achievement: Successful full enumeration of cousin primes up to the $10^{14}$ limit.

💎 Why is TSE Unique?

1. No Modular Arithmetic

Unlike traditional sieving algorithms, TSE replaces expensive MOD/DIV operations with simple integer additions ($n \leftarrow n+p$). This hardware-friendly approach eliminates the heavy computational overhead of division in GPU/HPC architectures.

2. Extreme Memory Efficiency

The canonical $N/3$ bit sieve structure has been reduced to an $N/6$ bit representation by leveraging the mathematical nature of $(p, p+2)$ and $(p, p+4)$ pairs. This allows processing 100 trillion numbers ($10^{14}$) using only 1.1 GB of VRAM.

3. Seamless Compactness & UI/UX

No Coding Knowledge Required: A fully menu-driven, interactive interface for researchers.
Smart Hardware Detection: Automatically analyzes system CPU and GPU specifications (Cores, Cache, VRAM).
Professional Reporting: Generates detailed performance metrics after every analysis.

📝 Sample Performance Analysis Report

TSE generates detailed reports showing the architectural efficiency of the system:

*************************** NEW REPORT ***********************
==============================================================
                PERFORMANCE ANALYSIS & REPORT
                     2026-01-17 15:11:49
==============================================================
 Engine Type        : GPU Segmented Sieve (Cuda Parallel.)
 Device             : NVIDIA GeForce RTX 3070
 Range Start        : 1
 Range End          : 1,000,000,000,000
 Type               : TWIN PRIME
 Total Process Time : 5 s 510 ms
 TOTAL PAIRS FOUND  : 1,870,585,220
 --------------------------------------------------------------
 Throughput         : 181.488 G-items/s
 CUDA Occupancy     : %83.3 (Architectural Efficiency)
 Speed (Decimal)    : 181488.203 Million/s
 Speed (Binary)     : 173080.638 Mi/s
 System RAM Usage   : 281 MB
 GPU VRAM Usage     : 1127 MB
 --------------------------------------------------------------
 >> 181,488,203,266 numbers checked per second
===============================================================
This report is the result of the TSE V.1.0.0 application.
************************** END OF REPORT **********************

*************************** NEW REPORT ***********************
==============================================================
                PERFORMANCE ANALYSIS & REPORT
                     2026-01-17 15:54:30
==============================================================
 Engine Type        : GPU Segmented Sieve (Cuda Parallel.)
 Device             : NVIDIA GeForce RTX 3070
 Range Start        : 1
 Range End          : 100,000,000,000,000
 Type               : TWIN PRIME
 Total Process Time : 2264 s 706 ms
 TOTAL PAIRS FOUND  : 135,780,321,665
 --------------------------------------------------------------
 Throughput         : 44.156 G-items/s
 CUDA Occupancy     : %83.3 (Architectural Efficiency)
 Speed (Decimal)    : 44155.842 Million/s
 Speed (Binary)     : 42110.292 Mi/s
 System RAM Usage   : 314 MB
 GPU VRAM Usage     : 1145 MB
 --------------------------------------------------------------
 >> 44,155,841,862 numbers checked per second
===============================================================
This report is the result of the TSE V.1.0.0 application.
************************** END OF REPORT **********************

*************************** NEW REPORT ***********************
==============================================================
                PERFORMANCE ANALYSIS & REPORT
                     2026-01-17 19:49:20
==============================================================
 Engine Type        : GPU Segmented Sieve (Cuda Parallel.)
 Device             : NVIDIA GeForce GTX 1650 Ti
 Range Start        : 1,000,000,000,000,000
 Range End          : 1,001,000,000,000,000
 Type               : TWIN PRIME
 Total Process Time : 348 s 447 ms
 TOTAL PAIRS FOUND  : 1,106,775,692
 --------------------------------------------------------------
 Throughput         : 2.870 G-items/s
 CUDA Occupancy     : %100.0 (Architectural Efficiency)
 Speed (Decimal)    : 2869.877 Million/s
 Speed (Binary)     : 2736.928 Mi/s
 System RAM Usage   : 279 MB
 GPU VRAM Usage     : 886 MB
 --------------------------------------------------------------
 >> 2,869,876,910 numbers checked per second
===============================================================
This report is the result of the TSE V.1.0.0 application.
************************** END OF REPORT **********************

*************************** NEW REPORT ***********************
==============================================================
                PERFORMANCE ANALYSIS & REPORT
                     2026-01-17 05:05:49
==============================================================
 Engine Type        : CPU Multi-Core Segmented (OMP Parallel.)
 Device             : Intel(R) Core(TM) i7-10750H CPU @ 2.60GHz
 Range Start        : 0
 Range End          : 100,000,000,000
 Type               : COUSIN PRIME
 Total Process Time : 12 s 177 ms
 TOTAL PAIRS FOUND  : 224,373,161
 --------------------------------------------------------------
 Throughput         : 8.212 G-items/s
 Compute Strategy   : High-Throughput Mode
 Speed (Decimal)    : 8212.203 Million/s
 Speed (Binary)     : 7831.767 Mi/s
 System RAM Usage   : 150 MB
 GPU VRAM Usage     : 0 MB
 --------------------------------------------------------------
 >> 8,212,203,334 numbers checked per second
===============================================================
This report is the result of the TSE V.1.0.0 application.
************************** END OF REPORT **********************

🚀 How to Use (Step-by-Step)

System Requirements

GPU: NVIDIA CUDA Compute Capability 3.5+ (RTX/GTX Series).
CPU: Intel/AMD x86-64 (with OpenMP support).
OS: Currently Windows 10/11 only.

Usage Steps

Run Tse_v100.exe.

The application will automatically detect your hardware (Cores, Cache, GPU, VRAM).

Select from the Main Menu:

[1] GPU MODE: Uses the CUDA engine for maximum performance.
[2] CPU MODE: Uses the multi-core statistical engine.
Enter Parameters: Start (N), End (M), and Prime Type (1: Twin, 2: Cousin).
Once the analysis is complete, press the Y key to save the results as TSE_Report_[Date].txt.

📊 Global Benchmarking & Contribution

We aim to build a comprehensive performance database across different hardware architectures. You can contribute to the development and scientific validation of the Turkish Sieve Engine:

Submit Your Benchmarks: If you run a test and select the "Save Results (Y)" option, the application will automatically generate an analysis_log.rtf (performance metrics) and an engine_config.txt (hardware/system specs).
- Please email these two files to bilgisoft.tr@gmail.com along with your name or nickname.
- We will publish verified results in our official Global Benchmark Table to showcase how TSE performs on various GPUs and CPUs worldwide.
Star the Project: If you are a researcher, academic, or enthusiast using this engine, please consider giving this repository a Star (⭐). Your support helps increase the project's visibility in the scientific community and encourages further development of the N/6 bit methodology.

📂 Repository Structure

src/ → Source code implementations (CUDA & OpenMP).
bin/ → Executable files (tse.exe).
docs/ → Academic paper (Zenodo PDF), figures, and documentation.
logs/ → Execution and performance logs.

🔮 Roadmapv1.1.0 (2026 H2):

Multi-GPU support (NVLink), GMP Integration (breaking the $2^{64}$ limit).

v2.0.0+: Distributed computing (MPI), AI-optimized sieving patterns, and FPGA support.

⚖️ Licensing & CitationAcademic Use:

Free of charge with full capacity but time-limited access for researchers and the scientific community.

Commercial Use:

Subject to a licensing agreement for enterprise integration and commercial use.

Details:

See the LICENSE.md file for more information.

⚖️ Citation

If you use the Turkish Sieve Engine or the N/6 Bit Methodology in your research, please cite the original work using the following format:

APA Style

ÇAKANLI, H. (2025). The Turkish Sieve Methodology: Deterministic Computation of Twin and Cousin Prime Pairs Using an N/6 Bit Data Structure (V.1.0.0). Zenodo. https://doi.org/10.5281/zenodo.18038661

💡 Other Styles (BibTeX, RIS, MLA, etc.)

You can export this citation in various formats directly from the official Zenodo page:
👉 View and Export Citations on Zenodo

DOI: 10.5281/zenodo.18038661

Contact & Licensing: 📧 bilgisoft.tr@gmail.com

🔬 Academic Metadata & Publication Details

The methodology behind this engine is formally documented as a scientific preprint. Below are the official publication details:

Document Title: The Turkish Sieve Methodology: Deterministic Computation of Twin and Cousin Prime Pairs Using an N/6 Bit Data Structure
Persistent Identifier (DOI): 10.5281/zenodo.18038661
Resource Type: Preprint (Scientific Paper)
Publisher: Zenodo
Primary Language: English
Release Date: 2025

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