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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

New Cullen primes


Author: Wilfrid Keller
Journal: Math. Comp. 64 (1995), 1733-1741, S39
MSC: Primary 11A51; Secondary 11A41, 11Y05
MathSciNet review: 1308456
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Abstract: Numbers of the forms $ {C_n} = n \cdot {2^n} + 1$ and $ {W_n} = n\cdot{2^n} - 1$ are both called Cullen numbers. New primes $ {C_n}$ are presented for $ n = 4713,5795,6611,18496$. For $ {W_n}$, several new primes are listed, the largest one having $ n = 18885$. Furthermore, all efforts made to factorize numbers $ {C_n}$ and $ {W_n}$ are described, and the result, the complete factorization for all $ n \leq 300$, is given in a Supplement.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1995-1308456-3
PII: S 0025-5718(1995)1308456-3
Keywords: Cullen numbers, factoring, large primes
Article copyright: © Copyright 1995 American Mathematical Society