Irregular primes and cyclotomic invariants to four million

Buhler, J.; Crandall, R.; Ernvall, R.; Metsänkylä, T.

doi:10.1090/S0025-5718-1993-1197511-5

Irregular primes and cyclotomic invariants to four million
HTML articles powered by AMS MathViewer

by J. Buhler, R. Crandall, R. Ernvall and T. Metsänkylä PDF

Math. Comp. 61 (1993), 151-153 Request permission

Abstract:

Recent computations of irregular primes, and associated cyclotomic invariants, were extended to all primes below four million using an enhanced multisectioning/convolution method. Fermat’s "Last Theorem" and Vandiver’s conjecture were found to be true for those primes, and the cyclotomic invariants behaved as expected. There is exactly one prime less than four million whose index of irregularity is equal to seven.

References

J. P. Buhler, R. E. Crandall, and R. W. Sompolski, Irregular primes to one million, Math. Comp. 59 (1992), no. 200, 717–722. MR 1134717, DOI 10.1090/S0025-5718-1992-1134717-4

Multidigit multiplication, the FFT, and Nussbaumer’s algorithm

Richard Crandall and Barry Fagin, Discrete weighted transforms and large-integer arithmetic, Math. Comp. 62 (1994), no. 205, 305–324. MR 1185244, DOI 10.1090/S0025-5718-1994-1185244-1
R. Ernvall and T. Metsänkylä, Cyclotomic invariants for primes to one million, Math. Comp. 59 (1992), no. 199, 249–250. MR 1134727, DOI 10.1090/S0025-5718-1992-1134727-7
Wells Johnson, Irregular primes and cyclotomic invariants, Math. Comp. 29 (1975), 113–120. MR 376606, DOI 10.1090/S0025-5718-1975-0376606-9
Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
D. H. Lehmer, Emma Lehmer, and H. S. Vandiver, An application of high-speed computing to Fermat’s last theorem, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 25–33. MR 61128, DOI 10.1073/pnas.40.1.25
Jonathan W. Tanner and Samuel S. Wagstaff Jr., New congruences for the Bernoulli numbers, Math. Comp. 48 (1987), no. 177, 341–350. MR 866120, DOI 10.1090/S0025-5718-1987-0866120-4