Authors and affiliations
An integer, n, is called a Frobenius probable prime with respect to a polynomial when it passes the Frobenius probable prime test. Composite integers that are Frobenius probable primes are called Frobenius pseudoprimes. Jon Grantham developed and analyzed a Frobenius probable prime test with quadratic polynomials. Using the Chinese Remainder Theorem and Frobenius automorphisms, we were able to extend Grantham’s results to some cubic polynomials. This case is computationally similar but more efficient than the quadratic case.
- Number fields
- Grantham, J. Frobenius Pseudoprimes, Mathematics of Computation, Vol. 234, 2000, 873–891.
- Grantham, J. A Probable Prime Test With High Confidence, Journal of Number Theory, Vol. 72, 1998, 32–47.
Cite this paperAPA
Buell, C. A., & Kimball, E. W. (2014). Frobenius pseudoprimes and a cubic primality test. Notes on Number Theory and Discrete Mathematics, 20(4), 11-20.Chicago
Buell, Catherine A., and Eric W. Kimball. “Frobenius Pseudoprimes and a Cubic Primality Test.” Notes on Number Theory and Discrete Mathematics 20, no. 4 (2014): 11-20.MLA
Buell, Catherine A., and Eric W. Kimball. “Frobenius Pseudoprimes and a Cubic Primality Test.” Notes on Number Theory and Discrete Mathematics 20.4 (2014): 11-20. Print.