Some prime numbers of the forms $2A3\sp{n}+1$ and $2A3\sp{n}-1$

On Some New Questions on the Distribution of Prime Numbers

have infinitely many solutions. If the well known hypothesis about prime twins is true, that is, if the equation pn+i—pn — 2 has infinitely many solutions, (1) and (2) of course are trivially satisfied. The first inequality of (2) is inserted only for the sake of completeness. I t follows from the well known fact that lim sup (pn+i—pn) = °° (since n\+2, n\+3, • • • , » ! + » are all composite)....

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Asymptotic behaviour of some infinite products involving prime numbers

The asymptotic behaviour of some entire functions defined via infinite products is investigated as the parameter z tends to infinity in the sector | arg z| < π. These functions arise in the distributions of the number of prime factors of integers and of the number of irreducible factors of monic polynomials over a finite field. Our approach is based on the Mellin transform with a suitable conto...

Asymptotic Behaviour of Some Infinite Products Involving Prime Numbers

Prime Slaughter: Playful Prime Numbers

Starting from the difficulty of creating playful representation of domain-specific abstract concepts, this study discusses the design of Prime Slaughter, a computer game aimed at facilitating individual sense-making of abstract mathematical concepts. Specifically the game proposes a transpositionmathematical concepts. Specifically the game proposes a transposition of primality and factorization...