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Some prime numbers of the forms $ 2A3\sp{n}+1$ and $ 2A3\sp{n}-1$


Authors: H. C. Williams and C. R. Zarnke
Journal: Math. Comp. 26 (1972), 995-998
MSC: Primary 10A25
DOI: https://doi.org/10.1090/S0025-5718-1972-0314747-X
MathSciNet review: 0314747
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Abstract: All primes of the form $ 2A{3^n} + 1$ and of the form $ 2A{3^n} - 1$, where $ 1 \leqq A \leqq 50$ and $ 1 \leqq n \leqq 325$, are found. Some large twin primes are also determined.


References [Enhancements On Off] (What's this?)

  • [1] H. Riesel, ``Lucasian criteria for the primality of $ N = h \cdot {2^n} - 1$,'' Math. Comp., v. 23, 1969, pp. 869-875. MR 41 #6773. MR 0262163 (41:6773)
  • [2] R. M. Robinson, ``A report on primes of the form $ k \cdot {2^n} + 1$ and on factors of Fermat numbers,'' Proc. Amer. Math. Soc., v. 9, 1958, pp. 673-681. MR 20 #3097. MR 0096614 (20:3097)
  • [3] H. C. Williams & C. R. Zarnke, ``A report on prime numbers of the forms $ M = (6a + 1){2^{2m - 1}} - 1$ and $ M' = (6a - 1){2^{2m}} - 1$,'' Math. Comp., v. 22, 1968, pp. 420-422. MR 37 #2680. MR 0227095 (37:2680)
  • [4] H. C. Williams, ``The primality of $ 2A{3^n} - 1$,'' Canad. Math. Bull., (To appear.) MR 0311559 (47:121)
  • [5] H. C. Williams, ``An algorithm for determining certain large primes,'' Proc. Second Louisiana Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, 1971, pp. 533-556. MR 0319874 (47:8415)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0314747-X
Keywords: Primes, twin primes, algorithm
Article copyright: © Copyright 1972 American Mathematical Society

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