Fermat number
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 = 1238926361552897 * 93461639715357977769163558199606896584051237541638188580280321. The ρ algorithm was a good choice for because the prime factor = 1238926361552897 is much smaller than the other factor. The factorization took 2 hours on a UNIVAC 1100/42.