Number theory and Group theory

Regarding the problem explained in the section "An open problem", we compute the percentage of integers until 10,000 that satisfy Condition 1 fixing one prime to be 2, 3, 5, 7 and 11. Here we provide the code that returns how many integers smaller than n do not satisfy Condition 1 if we fix one prime. It is possible to change the fixed prime, named aa in the code, by just changing it in the code (note that if we want one prime to be 2, then aa has to be 0 because it is the 0^th prime. 3 is the 1^th prime, and so on. Also, we use the BigInt library for large numbers that can be downloaded in the following page: https://mattmccutchen.net/bigint/.