NDLI: The Prime Number Graph

Content Provider	Scilit
Author	Pomerance, Carl
Copyright Year	1979
Description	Let denote the nth prime. The prime number graph is the set of lattice points , . 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 for all positive . By a similar argument, we show that there are infinitely many n for which {p_{n - i}}{p_{n + i}}$"> for all positive , thus verifying a conjecture of Selfridge. We make some new conjectures.
Related Links	https://www.ams.org/mcom/1979-33-145/S0025-5718-1979-0514836-7/S0025-5718-1979-0514836-7.pdf
Ending Page	408
Page Count	10
Starting Page	399
ISSN	00255718
e-ISSN	10886842
DOI	10.2307/2006053
Journal	Mathematics of Computation
Issue Number	145
Volume Number	33
Language	English
Publisher	Duke University Press
Publisher Date	1979-01-01
Access Restriction	Open
Subject Keyword	Logic Prime Number
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory Computational Mathematics

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The Prime Number Graph