The Prime Number Graph
نویسندگان
چکیده
Let pn denote the nth prime. The prime number graph is the set of lattice points (n, pn), n = 1, 2.We show that for every k there are k such points that are collinear. By considering the convex hull of the prime number graph, we show that there are infinitely many n such that 2pn < pn_¡ + Pn+Ifor all positive i < n. By a similar argument, we show that there are infinitely many n for which pn > pn-ipn+i for a" positive ' < ", thus verifying a conjecture of Selfridge. We make some new conjectures.
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