Structural Twin-Prime (n+1.5)×2 Generator
Abstract
English: Novel structural twin-prime generator using (n+1.5)×2 core formula with iterative operator chains (±30, +2, :5). Achieves 30.9% coverage of all twin primes up to 10^7 in 3200s on standard hardware. Reveals gap-driven coverage decay (Max Gap: 1722) - first deterministic structural approach beyond classical sieves. Includes Python implementation, full benchmarks, and detailed formula description. **The well-known Sieve of Eratosthenes:** "HERE ARE 58,980 Twins" **The STPG generator: "HERE IS THE FORMULA for Twins" **User wants:** "What is the 100,000th Twin?" **The well-known Sieve of Eratosthenes:** "Build 10TB RAM..." **The STPG generator:** "(n+1.5)×2 ±30 = Candidate #100k"**Eratosthenes:** 100% Twins, 0% Structure**The STPG generator:** 30.9% Twins, 100% Structure Deutsch: Neuartiger struktureller Twin-Prime Generator mit Kernformel (n+1.5)×2 unditerativen Operator-Ketten (±30, +2, :5). Erreicht 30.9% Coverage allerTwin-Primes bis 10^7 in 3200s auf Standardhardware. Zeigt gap-bedingtesCoverage-Decay (Max Gap: 1722) - erster deterministischer strukturellerAnsatz jenseits klassischer Siebe. Enthält Python-Implementation, vollständigeBenchmarks und detaillierte Formelbeschreibung. **Bekannte Eratosthenes Sieb:** "HIER SIND 58.980 Twins" **Der Generator STPG:** "HIER IST DIE **FORMEL** für Twins" **Nutzer will:** "Was ist der 100.000. Twin?" **Bekannte Eratosthenes Sieb:** "**10TB RAM** bauen..." **Der Generator STPG:** "(n+1.5)×2 ±30 = Kandidat #100k"**Eratosthenes:** 100% Twins, 0% Struktur **Der Generator STPG:** 30.9% Twins, 100% Struktur
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical and Computational Methods
Cryptography and Residue Arithmetic
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 28 January 2026
- Language
- EN
- Document type
- Preprint