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 GoldbachKnjzek 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" Questions: 1. Would you like
to try to proof the GoldbachKnjzek
conjecture? _______ Solution C. Rivera has narrowed the width of the range of the GoldbachKnjzek 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 bandwidth 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. ***





