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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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The 25th and 26th Mersenne primes
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by Curt Noll and Laura Nickel PDF
Math. Comp. 35 (1980), 1387-1390 Request permission

Abstract:

The 25th and 26th Mersenne primes are ${2^{21701}} - 1$ and ${2^{23209}} - 1$, respectively. Their primality was determined with an implementation of the Lucas-Lehmer test on a CDC Cyber 174 computer. The 25th and 26th even perfect numbers are $({2^{21701}} - 1)\;{2^{21700}}$ and $({2^{23209}} - 1)\;{2^{23208}}$, respectively.
References
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  • Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
    • D. H. LEHMER, "On Lucas’s test for the primality of Mersenne’s numbers," J. London Math. Soc., v. 10, 1935, pp. 162-165. D. H. LEHMER, Private communication with, University of California at Berkeley, Department of Mathematics, Berkeley, Calif. 94720. STEVE McGROGAN, Private communication with, 19450 Yuma Drive, Castro Valley, Calif. 94546. LAURA A. NICKEL & CURT L. NOLL, "The 25th Mersenne prime," Dr. Dobb’s Journal, v. 4, issue 6, p. 6. CURT L. NOLL, "Discovering the 26th Mersenne prime," Dr. Dobb’s Journal, v. 4, issue 6, pp. 4-5.
  • Bryant Tuckerman, The 24th Mersenne prime, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 2319–2320. MR 291072, DOI 10.1073/pnas.68.10.2319
    • BRYANT TUCKERMAN, Private communication with, International Business Machines Corporation, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598. S. WAGSTAFF, JR., Private communication with, University of Illinois, Urbana, Illinois 61801.
  • David Slowinski, Searching for the 27th Mersenne prime, J. Recreational Math. 11 (1978/79), no. 4, 258–267. MR 536930
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1387-1390
  • MSC: Primary 10A25
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583517-4
  • MathSciNet review: 583517