On using of weird number sequence in counting Beurling prime systems

Abstract

Beurling introduces the generalisation of the primes in the third decade of last century. He said in his work that any positive , increasiy real sequences {ri}∞ i=1 with r1 precisely qreatar than one called Beurling primes the fundamental Furthermore, the series of Beurling integers (or B-integers) could be generated by using the F-T-A. This work adapted the generalization Balanzarios work “Exampls of the generalised prime system“ where using the sequence of weird numbers to show that size of |N(x) – ax|, a > 0 is always less that the asymptotic behavior of πq(x).