In an earlier Report (NM-R9212, June 1992), two of us gave tables of factorizations of $a^n pm 1$ for $13 le a < 100$. The exponents~$n$ satisfied $a^n < 10^{255}$ if $a < 30$, and $n le 100$ if $a ge 30$. The factorizations were complete for $n le 46$, and the tables contained no composite numbers smaller than $10^{80}$. In this Report we update the original tables. The factorizations are now complete for $n le 58$, and there are no composite numbers smaller than $10^{86}$.

Department of Numerical Mathematics [NM]
Numerical mathematics

Brent, R.P, Montgomery, P.L, & te Riele, H.J.J. (1994). Update 1 to: Factorizations of $ a^ n pm 1,13 leq a < 100 $. Department of Numerical Mathematics [NM]. CWI.