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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Primes differing by a fixed integer
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by W. G. Leavitt and Albert A. Mullin PDF
Math. Comp. 37 (1981), 581-585 Request permission


It is shown that the equation $( \ast )\;{(n - 1)^2} - \sigma (n)\phi (n) = {m^2}$ is always solvable by $n = {p_1}{p_2}$ where ${p_1},{p_2}$ are primes differing by the integer m. This is called the "Standard" solution of $( \ast )$ and an m for which this is the only solution is called a "$^\ast$-number". While there are an infinite number of non $^\ast$-numbers there are many (almost certainly infinitely many) $^\ast$-numbers, including $m = 2$ (the twin prime case). A procedure for calculating all non $^\ast$-numbers less than a given bound L is devised and a table is given for $L = 1000$.
  • S. A. Sergušov, On the problem of prime-twins, Jaroslav. Gos. Ped. Inst. Učen. Zap. Vyp. 82 Anal. i Algebra (1971), 85–86 (Russian). MR 0480384
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 581-585
  • MSC: Primary 10L10; Secondary 10H15
  • DOI:
  • MathSciNet review: 628716