Distribution of irregular primes
نویسندگان
چکیده
منابع مشابه
Irregular primes to 163 million
We compute all irregular primes less than 163 577 856. For all of these primes we verify that the Kummer–Vandiver conjecture holds and that the λ-invariant is equal to the index of irregularity.
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The maxima and minima of sL(x)) — n(x), iR(x)) — n(x), and sL2(x)) — n2(x) in various intervals up to x = 8 x 10 are tabulated. Here n(x) and n2(x) are respectively the number of primes and twin primes not exceeding x, L(x) is the logarithmic integral, R(x) is Riemann's approximation to ir(x), and L2(x) is the Hardy-Littlewood approximation to ti"2(;c). The computation of the sum of inverses of...
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To understand the natural numbers, we must first understand the primes. Yet the behavior of the primes remains for the most part a mystery. For example, despite the efforts of many great mathematicians over hundreds of years, we still know very little about how the primes are distributed (scattered) throughout the natural numbers. The results and conjectures pertaining to the distribution of th...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1965
ISSN: 0019-2082
DOI: 10.1215/ijm/1256059295