Sieve Structures of Primorial Goldbach Complements

Key Points

• The aim is to explore the relationship between primorial complements and their coprime properties with smaller primes.
• Proved a pre-sieving property for every prime p > pk.
• Analyzed the integer N − p to establish coprimality with q ≤ pk.
• Developed a symmetry principle for sifted sets under the involution x → N − x.
• Demonstrated that primorial complements are coprime to all primes less than or equal to pk.
• Showed that this property eliminates local obstructions from smaller primes.
• Established a rigorous symmetry principle for the distribution of sifted sets.