Some prime numbers of the forms and
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: All primes of the form and of the form
, where
and
, are found. Some large twin primes are also determined.
- [1] Hans Riesel, Lucasian criteria for the primality of 𝑁=ℎ⋅2ⁿ-1, Math. Comp. 23 (1969), 869–875. MR 262163, https://doi.org/10.1090/S0025-5718-1969-0262163-1
- [2] Raphael M. Robinson, A report on primes of the form 𝑘⋅2ⁿ+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc. 9 (1958), 673–681. MR 96614, https://doi.org/10.1090/S0002-9939-1958-0096614-7
- [3] H. C. Williams and 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. 22 (1968), 420–422. MR 227095, https://doi.org/10.1090/S0025-5718-1968-0227095-2
- [4] H. C. Williams, The primality of 𝑁=2𝐴3ⁿ-1, Canad. Math. Bull. 15 (1972), 585–589. MR 311559, https://doi.org/10.4153/CMB-1972-101-7
- [5] H. C. Williams, An algorithm for determining certain large primes, Proceedings Second Louisiana Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1971) Louisiana State Univ., Baton Rouge, La., 1971, pp. 533–556. MR 0319874
Retrieve articles in Mathematics of Computation with MSC: 10A25
Retrieve articles in all journals with MSC: 10A25
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