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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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Factors of Fermat numbers and large primes of the form $k\cdot 2^{n}+1$
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by Wilfrid Keller PDF
Math. Comp. 41 (1983), 661-673 Request permission

Abstract:

A new factor is given for each of the Fermat numbers ${F_{52}},{F_{931}},{F_{6835}}$, and ${F_{9448}}$. In addition, a factor of ${F_{75}}$ discovered by Gary Gostin is presented. The current status for all ${F_m}$ is shown in a table. Primes of the form $k \cdot {2^n} + 1,k$ odd, are listed for $31 \leqslant k \leqslant 149$, $1500 < n \leqslant 4000$, and for $151 \leqslant k \leqslant 199$, $1000 < n \leqslant 4000$. Some primes for even larger values of n are included, the largest one being $5 \cdot {2^{13165}} + 1$. Also, a survey of several related questions is given. In particular, values of k such that $k\cdot {2^n} + 1$ is composite for every n are considered, as well as odd values of h such that $3h\cdot {2^n} \pm 1$ never yields a twin prime pair.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 41 (1983), 661-673
  • MSC: Primary 11Y05; Secondary 11A41, 11Y11
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0717710-7
  • MathSciNet review: 717710