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Irregular primes and cyclotomic invariants to four million. (English) Zbl 0789.11020

The first two authors and R. W. Sompolski [Math. Comput. 59, 717- 722 (1992; Zbl 0768.11009)] previously calculated all irregular pairs of primes less than 1 million. The present authors extend this to 4 million. They verify that, up to this bound, the following are true: Fermat’s Last Theorem, Vandiver’s Conjecture, and the Iwasawa \(\lambda\)-invariant equals the index of irregularity. One example of a prime with index of irregularity 7 was found, the previous highest being 6.

MSC:

11D41 Higher degree equations; Fermat’s equation
11R23 Iwasawa theory
11-04 Software, source code, etc. for problems pertaining to number theory
11B68 Bernoulli and Euler numbers and polynomials
65Y20 Complexity and performance of numerical algorithms
11Y55 Calculation of integer sequences
68Q25 Analysis of algorithms and problem complexity

Citations:

Zbl 0768.11009
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Full Text: DOI

References:

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