Having students try to generate their own random numbers can lead to much discovery learning as one tries to create 'patternlessness' from formulas. Developing an equidistribution test and runs test, plus other ideas for generating random numbers, is discussed, with computer programs given. (MNS)

Suggestions are given for having students write or modify computer programs for listing prime positive integers and continued fractions, to help them discover mathematical concepts. Sample programs are included. (MNS)