DIO 3 - Tuples for Special Numbers - I

3 dio Efikasnost.p65

3 dio Modno.p65

Primes in tuples I

We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker conjecture implies that there are infinitely often primes a bounded distance ap...

On the distribution of M-tuples of B-numbers

In the classical sense, the set B consists of all integers which can be written as a sum of two perfect squares. In other words, these are the values attained by norms of integral ideals over the Gaussian field Q(i) . G.J. Rieger (1965) and T. Cochrane / R.E. Dressler (1987) established bounds for the number of pairs (n, n+h) , resp., triples (n, n+1, n+2) of B -numbers up to a large real param...

The Special Tuberculosis Numbers