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There are only three S•P numbers!

A positive integer, n, which is equal to the sum, S, of its digits multiplied by their product, P, is called an S·P number. S. Parameśwaran gave three examples of such numbers in: and he conjectured that there are only a finite number of them. This was confirmed when several of us proved that each S·P number has at most 60 digits. There the matter rested for a time. Even if it were possible to test all numbers from 1 to 1060 at the rate of 1040 per second (far beyond the capacity of today’s fastest computer) it would take much longer than the estimated age of the universe to complete the task.