Volume 14, 2008, Number 3

Volume 14Number 1Number 2 ▷ Number 3 ▷ Number 4

Analysis of primes using right-end-digits and integer structure
Original research paper. Pages 1–10
J. V. Leyendekkers and A. G. Shannon
Full paper (86 Kb) | Abstract

Primes were separated according to the right-end-digits (REDs) and classes in the modular ring Z6. The primes are given by jR, where j is the number of consecutive integers with RED = R (for p = 37, R = 7 and j = 3, and so on). The rows of j in classes ̅26, ̅46 ⊂ Z6, that contain primes, are found to have the form ½n(an ± 1), a = 1, 3, 5. A total of 499 primes were generated for n = 1 to 80 for RED = 7. Similar results apply to REDs 1, 3 and 9. A scalar characteristic was detected in the row structure of j.

Note on polynomials taking infinitely many primes as their values
Original research paper. Pages 11–14
Mladen Vassilev-Missana and Peter Vassilev
Full paper (140 Kb) | Abstract

In the paper, the polynomials with integer coefficients are considered and a hypothetical sufficient condition for these polynomials to take infinitely many primes as their values is proposed. That provides an alternative equivalent variant of the famous Dirichlet’s theorem for infinitely many primes in arithmetic progressions. Also an interesting analogy between the behaviour of polynomial’s zeros and the integers for which the polynomial takes prime values is noted.

Three-dimensional extensions of Fibonacci sequences. Part 1
Original research paper. Pages 15–18
Krassimir T. Atanassov
Full paper (111 Kb)

Cycles of binomial coefficients
Original research paper. Pages 19–24
A. G. Shannon
Full paper (1785 Kb) | Abstract

This paper considers some properties of rising and falling factorials by analogy with some classic results in number theory for cycles of binomial coefficients.

Volume 14Number 1Number 2 ▷ Number 3 ▷ Number 4

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