Boris B. Benyaminov

collaborators

5 papers

math.NT2011

On an upper bound for the prime gap

Boris B. Benyaminov

We investigate logarithmic and square-root types of bounds for the general difference of two primes, $P_{k + q} - P_{k}$ , $k, q \in N$ .

math.NT2011

On primes amongst squares of naturals

Boris B. Benyaminov

We analyze the inequality $P_{k + 1} - P_{k} < 1, k \in N$ , discuss the existence of primes on arbitrary intervals $(r, s), r < s, r, s \in R$ , and finally add…

math.NT2011

Several new relations for the $n^{t h}$ prime number

Boris B. Benyaminov

We arrive at some new relations for the prime number $P_{n}$ , based on the logarithmic and absolute-value properties of the function $π (x)$ .

math.NT2011

Logarithmic and absolute-value like properties of $π (x)$ with applications

Boris B. Benyaminov

We derive properties of $π (x)$ reminiscent of those of the logarithm and absolute value functions. Two of these properties are similar to the relations defining the linearity of a…

math.NT2011

Distribution law for twin primes amongst naturals

Boris B. Benyaminov

A hypothesis is put forward regarding the function $π_{2} (x)$ which describes the distribution of twin primes in the set of natural numbers. The function $π_{2} (x)$ is tested by evalua…

On an upper bound for the prime gap

On primes amongst squares of naturals

Several new relations for the nth prime number

Logarithmic and absolute-value like properties of π(x) with applications

Distribution law for twin primes amongst naturals

Several new relations for the $n^{t h}$ prime number

Logarithmic and absolute-value like properties of $π (x)$ with applications