Problems & Puzzles: Conjectures
Conjecture 22. A stronger version of the Goldbach Conjecture
Mr. Rudolf Knjzek, from Austria, sent the following conjecture evidently related to the Goldbach Conjecture (GC):
I will call this statement the Goldbach-Knjzek conjecture.
Knjzek says "To proof this will proof GC. And I think this will be not so difficult, than proofing the original conjecture". Later he added "My conjecture says that you need not the small primes to satisfy GC"
1. Would you like
to try to proof the Goldbach-Knjzek
C. Rivera has narrowed the width of the range of the Goldbach-Knjzek conjecture to sqrt(N)<p<4*sqrt(N), for N>4. He does not know if this is worthwhile.
He also notices that k*sqrt(N)<=N/2, for N=>4*k^2. Accordingly, the new range means a true narrower band-width for N=>64 while for the rest of the range 4<N<64, sqrt(N)<p<4*sqrt(N) is a wider band than the original one.