Abstract
For an odd composite number n, let w(n) denote the least witness for n; that is, the least positive number w for which n is not a strong pseudoprime to the base w. It is widely conjectured, but not proved, that w(n) > 3 for infinitely many n. We show the stronger result that w(n) > (log n)1/(3 log log log n) for infinitely many n. We also show that there are finite sets of odd composites which do not have a reliable witness, namely a common witness for all of the numbers in the set.
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© 1994 Springer-Verlag Berlin Heidelberg
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Alford, W.R., Granville, A., Pomerance, C. (1994). On the difficulty of finding reliable witnesses. In: Adleman, L.M., Huang, MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58691-1_36
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DOI: https://doi.org/10.1007/3-540-58691-1_36
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