The prime number graph

Author:
Carl Pomerance

Journal:
Math. Comp. **33** (1979), 399-408

MSC:
Primary 10A25; Secondary 52A10

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514836-7

MathSciNet review:
514836

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Abstract: Let denote the *n*th 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 for all positive , thus verifying a conjecture of Selfridge. We make some new conjectures.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0514836-7

Article copyright:
© Copyright 1979
American Mathematical Society