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The problem of the least prime number in an arithmetic progression and its applications to Goldbach's conjecture
Shaohua Zhang
The problem of the least prime number in an arithmetic progression is one of the most important topics in Number Theory. In [11], we are the first to study the relations between th…
Dickson's conjecture on --An equivalent form of Green-Tao's conjecture
Shaohua Zhang
In [1], we give Dickson's conjecture on . In this paper, we further give Dickson's conjecture on and obtain an equivalent form of Green-Tao's conjecture [2]. Based on ou…
Notes on Dickson's Conjecture
Shaohua Zhang
In 1904, Dickson [5] stated a very important conjecture. Now people call it Dickson's conjecture. In 1958, Schinzel and Sierpinski [14] generalized Dickson's conjecture to the high…
On the Infinitude of Some Special Kinds of Primes
Shaohua Zhang
The aim of this paper is to try to establish a generic model for the problem that several multivariable number-theoretic functions represent simultaneously primes for infinitely ma…
On a Weakened Form of Polignac Conjecture
Shaohua Zhang
Polignac [1] conjectured that for every even natural number , there exist infinitely many consecutive primes and such that . A weakened…
W Sequences and the Distribution of Primes in Short Interval
Shaohua Zhang
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribu…