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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



New Cullen primes

Author: Wilfrid Keller
Journal: Math. Comp. 64 (1995), 1733-1741
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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Keywords: Cullen numbers, factoring, large primes
Article copyright: © Copyright 1995 American Mathematical Society