This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the incl...This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.展开更多
In this paper,we consider the generalized Moser-type inequalities,sayφ(n)≥kπ(n),where k is an integer greater than 1,φ(n)is Euler function andπ(n)is the prime counting function.Using computer,Pierre Dusart’s ine...In this paper,we consider the generalized Moser-type inequalities,sayφ(n)≥kπ(n),where k is an integer greater than 1,φ(n)is Euler function andπ(n)is the prime counting function.Using computer,Pierre Dusart’s inequality onπ(n)and Rosser-Schoenfeld’s inequality involvingφ(n),we give all solutions ofφ(n)=2π(n)andφ(n)=3π(n),respectively.Moreover,we obtain the best lower bound that Moser-type inequalitiesφ(n)>kπ(n)hold for k=2,3.As consequences,we show that every even integer greater than 210 is the sum of two coprime composite,every odd integer greater than 175 is the sum of three pairwise coprime odd composite numbers,and every odd integer greater than 53 can be represented as p+x+y,where p is prime,x and y are composite numbers satisfying that p,and x and y are pairwise coprime.Specially,we give a new equivalent form of Strong Goldbach Conjecture.展开更多
文摘This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.
基金the National Natural Science Foundation of China(11401050)Scientific Research Innovation Team Project Affiliated to Yangtze Normal University(2016XJTD01)。
文摘In this paper,we consider the generalized Moser-type inequalities,sayφ(n)≥kπ(n),where k is an integer greater than 1,φ(n)is Euler function andπ(n)is the prime counting function.Using computer,Pierre Dusart’s inequality onπ(n)and Rosser-Schoenfeld’s inequality involvingφ(n),we give all solutions ofφ(n)=2π(n)andφ(n)=3π(n),respectively.Moreover,we obtain the best lower bound that Moser-type inequalitiesφ(n)>kπ(n)hold for k=2,3.As consequences,we show that every even integer greater than 210 is the sum of two coprime composite,every odd integer greater than 175 is the sum of three pairwise coprime odd composite numbers,and every odd integer greater than 53 can be represented as p+x+y,where p is prime,x and y are composite numbers satisfying that p,and x and y are pairwise coprime.Specially,we give a new equivalent form of Strong Goldbach Conjecture.
