Where Do Random Numbers Come From?

   The random numbers generated in a computer or calculator are not truly random. They are not produced by sampling a physical process that contains a random process, such as flipping a coin or monitoring radioactive decay.

   Computer and calculator-generated random numbers are produced by computing an algorithm. An algorithm, by its very nature, contains no random processes. Still, these computer-generated random numbers pass most statistical tests and are, for most (but not all) practical purposes, random. Random numbers produced by an algorithm are more accurately called pseudo-random numbers.           

   The most commonly used algorithm for generating psuedo-random numbers is the linear congruential generator (LCG). The defining equation for a LCG is

x_n+1 = (ax_n + c )mod m

where x_n is called the seed, a is an integer constant called the multiplier, c (also an integer constant) is called the increment, and m is the modulus.
   The project can be viewed and downloaded by clicking on this link:

 https://scratch.mit.edu/projects/115898710/

    A four-page pdf document takes you through a paper and pencil exercise that explains the mathematics of a linear congruential generator and is available, free, on request. Send a request to grandadscience@gmail.com.