A new method for producing large Carmichael numbers

Author:
H. Dubner

Journal:
Math. Comp. **53** (1989), 411-414

MSC:
Primary 11A51; Secondary 11Y11

DOI:
https://doi.org/10.1090/S0025-5718-1989-0969484-8

MathSciNet review:
969484

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new method for producing large three-component Carmichael numbers is derived. Only two primes must be found simultaneously instead of three as in the "standard" method. For each set of two primes many third primes can be found. Several Carmichael numbers with more than 3000 digits are shown, with the largest having 3710 digits.

**[1]**J. Brillhard, D. H. Lehmer & J. L. Selfridge, "New primality criteria and factorizations of 1,"*Math. Comp.*, v. 29, 1975, pp. 620-647. MR**0384673 (52:5546)****[2]**J. Chernick, "On Fermat's simple theorem,"*Bull. Amer. Math. Soc.*, v. 45, 1939, pp. 269-274. MR**1563964****[3]**H. Dubner, Letter to S. S. Wagstaff, Jr., dated August 13, 1985.**[4]**H. Dubner & R. Dubner, "The development of a powerful low-cost computer for number theory applications,"*J. Recreational Math.*, v. 18, no. 2, 1985-1986, pp. 81-86.**[5]**D. E. Knuth,*The Art of Computer Programming, Vol. 2. Seminumerical Algorithms*, 2nd ed., Addison-Wesley, Reading, Mass., 1981, pp. 278-299. MR**633878 (83i:68003)****[6]**S. S. Wagstaff, Jr., "Large Carmichael numbers,"*Math. J. Okayama Univ.*, v. 22, 1980, pp. 33-41. MR**573668 (82c:10007)****[7]**S. Woods & J. Huenemann, "Larger Carmichael numbers,"*Comput. Math. Appl.*, v. 8, no. 3, 1982, pp. 215-216. MR**662584 (83f:10017)**

Retrieve articles in *Mathematics of Computation*
with MSC:
11A51,
11Y11

Retrieve articles in all journals with MSC: 11A51, 11Y11

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1989-0969484-8

Article copyright:
© Copyright 1989
American Mathematical Society