Authors: Marius Coman
The study of the power of primes was for me a constant probably since I first encounter “Fermat’s last theorem”. The desire to find numbers with special properties, as is, say, Hardy-Ramanujan number, was another constant. In this paper I present a class of numbers, i.e. the numbers of the form n = 505 + 1008*k, where k positive integer, which, despite the fact that they don’t seem to be, prima facie, “special”, seem to have a strong connection with the powers of primes: for a lot of values of k (I show in this paper that for nine from the first twelve and I conjecture that for an infinity of the values of k), there exist p and q primes such that p^2 – q^2 + 1 = n. The special nature of the numbers of the form 505 + 1008*k is also highlight by the fact that they are (all the first twelve of them, as much I checked) primes or g/s-integers or c/m-integers (I define in Addenda to this paper the two new notions mentioned).
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[v1] 2015-04-20 08:40:39
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