منابع مشابه
Sieves of Dimension 1 +
with fκ(s) as large as possible (resp. Fκ(s) as small as possible) given that the above inequality holds for all choices of A satisfying (1). Selberg [2] has shown (in a much more general context) that the functions fκ(s), Fκ(s) are continuous, monotone, and computable for s > 1, that they do not change if we replace (1) with (2), and that they tend to 1 exponentially as s goes to infinity. Mor...
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We describe our single-instruction multiple data (SIMD) implementation of the multiple polynomial quadratic sieve integer factoring algorithm. On a 16K MasPar massively parallel computer, our implementation can factor 100 digit integers in a few days. Its most notable success was the factorization of the 110-digit RSA-challenge number, which took about a month.
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Zeolite and zeolite-like molecular sieves are being used in a large number of applications such as adsorption and catalysis. Achievement of the long-standing goal of creating a chiral, polycrystalline molecular sieve with bulk enantioenrichment would enable these materials to perform enantioselective functions. Here, we report the synthesis of enantiomerically enriched samples of a molecular si...
متن کاملTwo Compact Incremental Prime Sieves
A prime sieve is an algorithm that finds the primes up to a bound n. We say that a prime sieve is incremental, if it can quickly determine if n+1 is prime after having found all primes up to n. We say a sieve is compact if it uses roughly √ n space or less. In this paper we present two new results: • We describe the rolling sieve, a practical, incremental prime sieve that takes O(n log logn) ti...
متن کاملSelmer Group Heuristics and Sieves
In the past decade or so, the most elementary of the sieve methods of analytic number theory has been adapted to a geometric setting. In this geometric setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over Z. We will present the method and some of the results that have been proved using it. For instance, the prob...
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ژورنال
عنوان ژورنال: IEEE Transactions on Terahertz Science and Technology
سال: 2018
ISSN: 2156-342X,2156-3446
DOI: 10.1109/tthz.2017.2762292