I suggest glancing at two papers:
Hagedorn, Thomas. "Computation of Jacobsthal’s function $h(n)$ for $n< 50$." Mathematics of Computation 78.266 (2009): 1073-1087.
Hajdu, L., and N. Saradha. "Disproof of a conjecture of Jacobsthal." Mathematics of Computation 81.280 (2012): 2461-2471.
Both of them describe somewhat massive projects which involve a lot of computation. They give algorithmic descriptions as well as some sample computations. Although I personally want more, they provide enough detail that I do not question the validity of their work. You might use them as examples for how to write up your results.
Gerhard "The Computer Says So, QED" Paseman, 2015.07.25
