Introduction to Cryptography with Coding Theory, 3rd Edition

C.6 Examples for Chapter 9

Example 22

Two functions, nextprime and randprime, can be used to generate prime numbers. The function nextprime takes a number $n$ as input and attempts to find the next prime after $n$. The function randprime takes a number $n$ as input and attempts to find a random prime between $1$ and $n$. It uses the Miller-Rabin test described in Chapter 9.

>> nextprime(346735)

ans =
   346739

>> randprime(888888)

ans =
   737309

For larger inputs, use symbolic mode:

>> nextprime(10^sym(60))

ans =
   1000000000000000000000000000000000000000000000000000000000007

>> randprime(10^sym(50))

ans =
   58232516535825662451486550708068534731864929199219

It is interesting to note the difference that the ’ ’ makes when entering a large integer: