Primality testing revisited
@inproceedings{Davenport1992PrimalityTR, title={Primality testing revisited}, author={James H. Davenport}, booktitle={International Symposium on Symbolic and Algebraic Computation}, year={1992} }
Rabin’s algorithm is commonly used in computer algebra systems and elsewhere for primality testing. This paper presents an experience with this in the Axiom* computer algebra system. As a result of this experience, we suggest certain strengthenings of the algorithm.
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References
SHOWING 1-10 OF 26 REFERENCES
Distributed Primality Proving and the Primality of (23539+1)/3
- Mathematics, Computer ScienceEUROCRYPT
- 1990
The successful attempt at proving the primality of the l065-digit (23539+1)/3, the first ordinary Titanic prime, is described.
Explicit bounds for primality testing and related problems
- Mathematics
- 1990
Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits…
Analytic methods in the analysis and design of number-theoretic algorithms
- Computer Science, Mathematics
- 1985
This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic…
On strong pseudoprimes to several bases
- Mathematics
- 1993
With Y'k denoting the smallest strong pseudoprime to all of the first k primes taken as bases we determine the exact values for 5, q6, q7, q8 and give upper bounds for V/9, / W t,' 1 . We discuss the…
Statistical evidence for small generating sets
- Computer Science, Mathematics
- 1993
This work gives additional evidence, independent of the ERH, that primality testing can be done in deterministic polynomial time; if the bound on G(n) is correct, there is a deterministic primality test using O(log n)2 multiplications modulo n.
Modifications 18459366157::I, 21276028621::I ]::(List I) O(log4N) Modifications
- 1980
Pinch 1993] and Jaeschke 1993] Modiications The following global declarations are made
- Pinch 1993] and Jaeschke 1993] Modiications The following global declarations are made
- 1980