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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The prime number graph
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by Carl Pomerance PDF
Math. Comp. 33 (1979), 399-408 Request permission


Let ${p_n}$ denote the nth prime. The prime number graph is the set of lattice points $(n,{p_n})$, $n = 1,2, \ldots$. 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 $2{p_n} < {p_{n - i}} + {p_{n + i}}$ for all positive $i < n$. By a similar argument, we show that there are infinitely many n for which $p_n^2 > {p_{n - i}}{p_{n + i}}$ for all positive $i < n$, thus verifying a conjecture of Selfridge. We make some new conjectures.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 399-408
  • MSC: Primary 10A25; Secondary 52A10
  • DOI:
  • MathSciNet review: 514836