Paper 1: Some computational experiments in number theory by Wieb Bosma The code for this paper takes around 68,000 seconds to run on a 64-bit 2.6GHz AMD processor. The vast majority of this time (over 66,000 seconds) is spent on case c = 10 of the first example from section 2. Due to the random numbers used in the first example from section 2, results may vary from those shown in the paper. For instance, some runs find a solution for c = 8 using divisors of 50400 (better than shown), and many require divisors of 30240 for c = 7 (worse than shown). Changes since book release: V2.12: A minor change was made to the function 'permcharmat'; it now uses 'Eltseq' on the permutation character rather than explicit indexing. This is the more natural Magma idiom.