# Challenge: Smith Numbers

2

This question was written by the University of Virginia, but I found it to be an interesting challenge.

While skimming his phone directory in 1982, Albert Wilansky, a mathematician of Lehigh University, noticed that the telephone number of his brother-in-law H. Smith had the following peculiar property: The sum of the digits of that number was equal to the sum of the digits of the prime factors of that number. Got it? Smith’s telephone number was 493-7775. This number can be written as the product of its prime factors in the following way:

`4937775 = 3·5·5·65837 `

The sum of all digits of the telephone number is

`4 + 9 + 3 + 7 + 7 + 7 + 5 = 42`

and the sum of the digits of its prime factors is equally

`3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42`

Wilansky was so amazed by his discovery that he named this type of numbers after his brother-in-law: Smith numbers. As this observation is also true for every prime number, Wilansky decided later that a (simple and unsophisticated) prime number is not worth being a Smith number and he excluded them from the deﬁnition.
Wilansky published an article about Smith numbers in the Two Year College Mathematics Journal and was able to present a whole collection of diﬀerent Smith numbers: For example, 9985 is a Smith number and so is 6036. However, Wilansky was not able to give a Smith number which was larger than the telephone number of his brother-in-law.

It is your task to ﬁnd Smith numbers which are larger than 4937775.

Here at PlanckTime if we're gonna do it, we're gonna do it big.

Find the next 100, or more, Smith numbers larger than 4937775.

"Computer science is no more about computers than astronomy is about telescopes."
~ Edsger W. Dijkstra

3

Solution:-

This is my code:
https://github.com/ldhmachin/Smith-Numbers/

These are the next 100 numbers proceeding 4937775.

"Computer science is no more about computers than astronomy is about telescopes."
~ Edsger W. Dijkstra

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