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Primality Testing Revisited
, 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. Introduction It is customary ..."
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. 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. Introduction It is customary in computer algebra to use the algorithm presented by Rabin [1980] to determine if numbers are prime (and primes are needed throughout algebraic algorithms). As is well known, a single iteration of Rabin's algorithm, applied to the number N , has probability at most 0.25 of reporting "N is probably prime", when in fact N is composite. For most N , the probability is much less than 0.25. Here, "probability" refers to the fact that Rabin's algorithm begins with the choice of a "random" seed x, not congruent to 0 modulo N . In practice, however, true randomness is hard to achieve, and computer algebra systems often use a fixed set of x  for example Axiom release 1 uses the set f3; 5; 7; 11;...
ABSOLUTE QUADRATIC PSEUDOPRIMES
"... Abstract. We describe some primality tests based on quadratic rings and discuss the absolute pseudoprimes for these tests. 1. ..."
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Abstract. We describe some primality tests based on quadratic rings and discuss the absolute pseudoprimes for these tests. 1.