We gloss over the term, relatively prime, in our quest to understand numbers. A number is prime if it is relatively prime with all numbers: this seems to be the only reason to define a new term for the old situation of two numbers which have a greatest common denominator of one. A subset of GC1 is (a,a+1).
It seems quite clear that people who find themselves facing a mystery don't like to think that others who have pierced it cannot share what they know except to those who have spent a lifetime contemplating numbers.
We need to look at things that have patterns and at things that do not; we might then refer to chaos numbers. Determining the whether a number is chaos is easy (but slow). Multiplying such a number by itself a chaotic number of times produces a number with many factors.
n * c1 = m * c2 + n
This recalls the rule of three (or nine); obviously, then, c1 = c2 * d + 1.