Introduction Let p be a prime number.
If a number r can be found that satisfies these conditions, then p must be a prime number. The values of these functions for each admissible n or p is also of theoretical interest, in particular in what concerns their rate of growth. Our program records the number of times each one of those values occurred, as well as the value of p for which they first occur. We have used a modified segmented sieve of Eratosthenes to record, for each integer, its largest factor not larger than its square root. A Linux-only version is also in use.