I've noticed that for the smaller primes, it is possible to state each element of its reduced residue class as a simple equation in terms of the factors of the primorial.
For example, consider the primorial $5\# = 30$
The reduced residue class is $\{1,7,11,13,17,19,23,29\}$
Each of these elements can be expressed as a simple equation in terms of the factors of the primorial.
- 1 = $\frac{30}{5} - 5$
- 7 = $\frac{30}{3} - 3$
- 11 = $\frac{30}{5} + 5$
- 13 = $\frac{30}{2} - 2$
- 17 = $\frac{30}{2} + 2$
- 19 = $\frac{30}{2} + 2*2$
- 23 = $\frac{30}{2} + 2*2*2$
- 29 = $30 - 1$
Is this always the case? Is there a point where this stops being true?