The pseudoprimes to 25⋅10⁹
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This article is published in Mathematics of Computation.The article was published on 1980-07-01 and is currently open access. It has received 115 citations till now. The article focuses on the topics: Strong pseudoprime & Euler pseudoprime.read more
Citations
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There are infinitely many Carmichael numbers
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Explicit bounds for primality testing and related problems
TL;DR: In this article, it was shown that if the Extended Riemann Hypothesis holds, a composite number m has a witness for its compositeness (in the sense of Miller or Solovay-Strassen) that is at most 2 log 2m.
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Average case error estimates for the strong probable prime test
TL;DR: In this paper, the authors consider a procedure that chooses k-bit odd numbers independently and from the uniform distribution, subjects each number to t independent iterations of the strong probable prime test (Miller-Rabin test) with randomly chosen bases, and outputs the first number found that passes all t tests.
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On the distribution of pseudoprimes
TL;DR: In this paper, it was shown that VP(x) = x * L(x)-I+?(l) for large x, an improvement on the 1956 work of Erdos.
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Popular values of euler's function
TL;DR: In this article, the maximal order of the Euler's function for a natural number m is studied, where m denotes the number of integers n with o(n) = m, where o denotes Euler function.
References
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Riemann's hypothesis and tests for primality
TL;DR: It is shown that a class of functions which includes the Euler phi function are computationally equivalent to factoring integers.
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A Fast Monte-Carlo Test for Primality
Robert Solovay,Volker Strassen +1 more
TL;DR: A uniform distribution a from a uniform distribution on the set 1, 2, 3, 4, 5 is a random number and if a and n are relatively prime, compute the residue varepsilon.
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On the number of positive integers $\leq x$ and free of prime factors $>y$
TL;DR: The final author version and the galley proof are versions of the publication after peer review and the final published version features the final layout of the paper including the volume, issue and page numbers.