The algorithm is very fast for numbers with small factors, but slower in cases where all factors are large. The ρ algorithm's most remarkable success was the factorization of the [[Fermat number]] {{math|''F''<sub>8</sub>}} = 1238926361552897 * × 93461639715357977769163558199606896584051237541638188580280321.<ref name="FotEFN">{{cite journal |last1=Brent |first1=R.P. |last2=Pollard |first2=J. M. |year=1981 |title=Factorization of the Eighth Fermat Number |journal=Mathematics of Computation |volume=36 |issue=154 |pages=627–630 |doi=10.2307/2007666|doi-access=free }}</ref> The ρ algorithm was a good choice for {{math|''F''<sub>8</sub>}} because the prime factor {{mvar|p}} = 1238926361552897 is much smaller than the other factor. The factorization took 2 hours on a [[UNIVAC]] [[UNIVAC 1110|1100/42]].<ref name="FotEFN" />
