The number of prime divisors of certain Mersenne numbers
نویسندگان
چکیده
منابع مشابه
Sums of Prime Divisors and Mersenne Numbers
The study of the function β(n) originated in the paper of Nelson, Penney, and Pomerance [7], where the question was raised as to whether the set of Ruth-Aaron numbers (i.e., natural numbers n for which β(n) = β(n+ 1)) has zero density in the set of all positive integers. This question was answered in the affirmative by Erdős and Pomerance [5], and the main result of [5] was later improved by Po...
متن کاملDivisors of Mersenne Numbers By Samuel
We add to the heuristic and empirical evidence for a conjecture of Gillies about the distribution of the prime divisors of Mersenne numbers. We list some large prime divisors of Mersenne numbers Mp in the range 17000 < p < 105.
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Let P (k) be the largest prime factor of the positive integer k. In this paper, we prove that the series ∑ n≥1 (log n)α P (2n − 1) is convergent for each constant α < 1/2, which gives a more precise form of a result of C. L. Stewart of 1977.
متن کاملOn an Invariant of Divisors of Mersenne Number
where p is prime. In our paper we use the latter name. In this form numbers Mp at the first time were studied by Marin Mersenne (1588-1648) at least in 1644 (see in [1, p.9] and a large bibliography there). In our paper we show that all composite Mersenne numbers belong to a class S of pseudoprimes of base 2 which is a subclass of super-Poulet pseudoprimes. Analysis of properties of pseudoprime...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1967
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1967-0223320-1