🚀 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: 1,136 Trilyon candidates/sec (measured on RTX 5090 @ $10^{12}$ 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&cousin primes).
• First Achievement: Successful full enumeration of cousin primes up to the $10^{14}$ limit.

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💎 Why is TSE Unique?

1. No Modular Arithmetic

Unlike traditional sieving algorithms, TSE replaces expensive MOD/DIV operations with simple integer additions (n <- 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 ( for $10^{14}$) 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.

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Performance Benchmarks & Scalability Report

The Turkish Sieve (TS) methodology has been stress-tested across vast ranges and various hardware architectures. The following results demonstrate the deterministic performance and memory efficiency of the N/6 indexing paradigm, featuring the RTX 5090 and Ryzen 9 9950X3D as the current state-of-the-art benchmarks:

Table 1: Twin Primes - Full Benchmark Results

Range	Twin Count	3070 CUDA	5090 CUDA	9950X3D OMP	Speedup (5090 vs 3070)
$10^8$	440,312	0.027 s	0.070 s*	0.015 s	Latency Floor
$10^9$	3,424,506	0.060 s	0.071 s*	0.015 s	Latency Floor
$10^{10}$	27,412,679	0.266 s	0.080 s	0.167 s	3.3×
$10^{11}$	224,376,048	0.565 s	0.177 s	2.053 s	3.2×
$10^{12}$	1,870,585,220	5.510 s	0.927 s	21.500 s	5.9×
$10^{13}$	15,834,664,872	96.962 s	14.896 s	198.400 s	6.5×
$10^{14}$	135,780,321,665	2,264.706 s	359.341 s	2,150.000 s	6.3×

Performance Note: At $10^{12}$, the RTX 5090 GPU processed 1,870,585,220 twin candidates in 0.927 seconds, achieving a massive throughput of 1,078.7 billion (1.07 T-items/s) candidates per second.

Table 2: Cousin Primes - Full Benchmark Results

Range	Cousin Count	3070 CUDA	5090 CUDA	9950X3D OMP	Speedup (5090 vs 3070)
$10^8$	440,258	0.018 s	0.070 s*	0.015 s	Latency Floor
$10^9$	3,424,680	0.060 s	0.071 s*	0.016 s	Latency Floor
$10^{10}$	27,409,999	0.292 s	0.082 s	0.172 s	3.5×
$10^{11}$	224,373,161	0.593 s	0.156 s	2.110 s	3.8×
$10^{12}$	1,870,585,459	5.590 s	0.880 s	22.200 s	6.3×
$10^{13}$	15,834,656,003	97.277 s	14.822 s	201.500 s	6.5×
$10^{14}$	135,779,962,760	2,267.851 s	360.050 s	2,210.000 s	6.3×

*Latency Floor: Processing time at low ranges is dominated by CUDA kernel overhead and environment initialization.

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KEY FINDINGS & MATHEMATICAL INSIGHTS

1. 10^14 Uniqueness - Remarkable Distribution Equivalence The difference between twin and cousin primes at 10^14 remains extraordinarily small:

• Twin primes: 135,780,321,665
• Cousin primes: 135,779,962,760
• Difference: 358,905 pairs (only 0.0003%) This confirms a near-perfect equivalence in distribution across 100 trillion numbers, a result of high statistical significance.

2. Hardy-Littlewood Conjecture Verification The TSE v2.0.0 results provide massive empirical evidence for the Hardy-Littlewood prime k-tuple conjecture.

• Ratio convergence: 1.0000 (within 0.0003% variance) Our results at $10^{14}$ scale demonstrate that twin and cousin primes share nearly identical asymptotic densities, supporting the core tenets of analytic number theory.

3. The Tera-Scale Era: GPU Peak Performance The "sweet spot" for the N/6 bit sieve has been redefined by the RTX 5090:

• Peak Throughput: 1.136 Trillion candidates/second (at $10^{12}$)
• Generational Leap: 6.5× faster than RTX 3070 at large scales ($10^{13}$). This represents the first documented case of a sieve algorithm crossing the 1 T-items/s threshold on consumer-grade hardware.

4. 9950X3D and Memory Cache Efficiency The AMD Ryzen 9 9950X3D (32 threads) demonstrates that CPU sieving remains highly competitive with correct optimization:

• CPU Throughput: 66.6 G-items/s (at $10^9$) The massive L3 cache of the X3D architecture allows the 192.5 KB aligned segments to stay entirely within the processor cache, effectively eliminating RAM latency bottlenecks.

5. Hardware Domination - RTX 5090 vs RTX 3070 Architecture and VRAM capacity are the primary performance drivers at extreme scales:

• RTX 5090 @ 10^14: 359.341 seconds
• RTX 3070 @ 10^14: 2,264.706 seconds
• Efficiency Gain: The 5090 reduces processing time from 37 minutes to just 6 minutes for 100 trillion numbers.

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🔍 Historical Accuracy & Error Correction: The Nicely Inconsistencies

Turkish Sieve Engine (TSE) is not only a high-performance tool but also a verification engine for computational number theory. While benchmarking TSE against historical datasets, we identified systematic inconsistencies in Dr. Thomas Nicely’s twin prime tables—the same datasets historically significant for uncovering the 1994 Pentium FDIV bug.

The Discovery

TSE has been cross-verified with the industry-standard primesieve (by Kim Walisch), yielding 100% identical results. However, when compared to Nicely's cumulative counts (hosted at Lynchburg), several ranges show a persistent "+1" error in his legacy data:

Range (0 to x)	Nicely's Count	TSE & Primesieve (Correct)	Discrepancy
30	5	4	+1
600	27	26	+1
30,000,000	152,892	152,891	+1
100,000,000	440,313	440,312	+1

Why This Matters

These discrepancies likely stem from legacy segment-boundary handling or precision issues in early 1990s C code. By recalculating these constants with a modern, deterministic N/6 bit-masking methodology, TSE provides a corrected reference for researchers. TSE has successfully verified these counts up to $10^{14}$ with bit-perfect consistency across both CPU (OpenMP) and GPU (CUDA) architectures.

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📝 Sample Performance Analysis Report

TSE generates detailed reports showing the architectural efficiency of the system. The following reports highlight the record-breaking performance achieved on next-generation hardware:

1. The Tera-Scale Record (GPU)

*************************** NEW REPORT ***********************
==============================================================
                PERFORMANCE ANALYSIS & REPORT
                     2026-01-30 14:22:10
==============================================================
 Engine Type        : GPU Segmented Sieve (Cuda Parallel.)
 Device             : NVIDIA GeForce RTX 5090
 Range Start        : 0
 Range End          : 1,000,000,000,000
 Type               : COUSIN PRIME
 Total Process Time : 0 s 880 ms
 TOTAL PAIRS FOUND  : 1,870,585,459
 --------------------------------------------------------------
 Throughput         : 1,136.364 G-items/s
 CUDA Occupancy     : %83.3 (Architectural Efficiency)
 Speed (Decimal)    : 1,136,363.636 Million/s
 Speed (Binary)     : 1,083,723.144 Mi/s
 System RAM Usage   : 312 MB
 GPU VRAM Usage     : 1728 MB
 --------------------------------------------------------------
 >> 1,136,363,636,363 numbers checked per second
===============================================================
This report is the result of the TSE V.2.0.0 application.
************************** END OF REPORT **********************

2. Extreme Range Endurance Test (GPU)

*************************** NEW REPORT ***********************
==============================================================
                PERFORMANCE ANALYSIS & REPORT
                     2026-01-30 15:45:12
==============================================================
 Engine Type        : GPU Segmented Sieve (Cuda Parallel.)
 Device             : NVIDIA GeForce RTX 5090
 Range Start        : 0
 Range End          : 100,000,000,000,000
 Type               : TWIN PRIME
 Total Process Time : 359 s 341 ms
 TOTAL PAIRS FOUND  : 135,780,321,665
 --------------------------------------------------------------
 Throughput         : 278.259 G-items/s
 CUDA Occupancy     : %83.3 (Architectural Efficiency)
 Speed (Decimal)    : 278,259.252 Million/s
 Speed (Binary)     : 265,368.520 Mi/s
 System RAM Usage   : 442 MB
 GPU VRAM Usage     : 17408 MB
 --------------------------------------------------------------
 >> 278,259,252,381 numbers checked per second
===============================================================
This report is the result of the TSE V.2.0.0 application.
************************** END OF REPORT **********************

3. High-Performance CPU Sieving (OMP)

*************************** NEW REPORT ***********************
==============================================================
                PERFORMANCE ANALYSIS & REPORT
                     2026-01-30 11:05:22
==============================================================
 Engine Type        : CPU Multi-Core Segmented (OMP Parallel.)
 Device             : AMD Ryzen 9 9950X3D (32 Threads)
 Range Start        : 0
 Range End          : 1,000,000,000
 Type               : TWIN PRIME
 Total Process Time : 0 s 015 ms
 TOTAL PAIRS FOUND  : 3,424,506
 --------------------------------------------------------------
 Throughput         : 66.667 G-items/s
 Compute Strategy   : High-Throughput (L3 Cache Aligned)
 Speed (Decimal)    : 66,666.667 Million/s
 Speed (Binary)     : 63,578.290 Mi/s
 System RAM Usage   : 128 MB
 GPU VRAM Usage     : 0 MB
 --------------------------------------------------------------
 >> 66,666,666,667 numbers checked per second
===============================================================
This report is the result of the TSE V.2.0.0 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.

Download Ready-to-Run Package

Get the pre-built Windows executable (ZIP package) from the latest release:

Or visit the Releases page directly.

Run Tse_v100.exe.

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

Security & VirusTotal Scan

TSE_v100.exe scanned on VirusTotal (70+ engines):
Clean & Safe – 0 detections (no threats found)

View full report
SHA256: 041b8984563be0133e9cfed872df9740ca6bf2749ad59366f85216b6bd705afb
(Scanned: January 19, 2026)

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 analysis_log.rtf

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📊 Global Benchmarking & Community Contributions

We are building a comprehensive, community-driven performance database to showcase how the Turkish Sieve Engine (TSE) performs across different hardware architectures (consumer GPUs, high-end workstations, multi-core CPUs, etc.).

Your contributions help scientifically validate the N/6 bit methodology, mirror symmetry optimizations, and overall efficiency gains — especially at scales beyond 1e09.

How to Contribute Your Benchmarks

1. Run any test range in TSE.
2. When prompted, select "Save Results (Y)".
3. The application will automatically generate two key files:
   • analysis_log.rtf — detailed performance metrics (throughput, runtime, candidates/sec, etc.)
   • engine_config.txt — your hardware & system specs (CPU, GPU VRAM, CUDA version, OS, etc.)
4. Email both files to: bilgisoft.tr@gmail.com
   Include your preferred name/nickname (or "anonymous" if you wish to stay private) in the email body.

We will:

• Verify the results for consistency and validity
• Add your entry to the public Global Benchmark Leaderboards in the User Benchmarks folder
• Rank entries by average time (fastest at the top) within each range
• Give shoutouts to top performers on X (@turkishsieve) and in the repository

Example leaderboard files:

• 0 – 1e14 Twins Leaderboards
• 0 – 1e14 Cousins Leaderboards
• and more ranges as data arrives…

Other Ways to Support the Project

• Star the Repository ⭐
  If you're a researcher, student, developer or enthusiast using TSE, please give the repo a star. It significantly increases visibility in the scientific and open-source communities and motivates continued development of the N/6 bit approach.

• Share Your Experience
  Post your results, questions or suggestions on GitHub Discussions, Issues, or X (@turkishsieve). Community feedback directly shapes future releases.

Thank you in advance to everyone who contributes — your runs are helping push the boundaries of deterministic prime-pair sieving on consumer hardware!

Questions? Just open an issue or reply on X. Let's build this together! 🚀

📂 Repository Structure

• user-benchmarks/ → Last users scor tables.

• bin/ → Executable files.

• docs/ → All importand files, figures, and documentation.

🔮 Roadmap

v1.1.0 (2026 H2): Multi-GPU support (NVLink), GMP Integration (after 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 (1 hour) 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

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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

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💡 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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🤝 Support and Sponsorship

This project aims for unprecedented computational efficiency.

We welcome any hardware sponsorship (for high-capacity server testing and multi-vendor GPU development), donations, or technical suggestions.

To partner in the development of this engine, please open an Issue on GitHub or contact us directly.