Let $q, r \in \mathbb{P}$ and $r$ is the next prime to $q$.

What is the **multiplicative order** of $r$ modulo $\displaystyle\bigg( \prod_{\substack{p \leq q \\\text{p prime}}} p \bigg)$ ?

In other word what is the smallest $k \in \mathbb{N}^*$ verifying : $$r^k = 1 \pmod{\prod_{\substack{p \leq q \\\text{p prime}}} p}$$

Using **Euler theorem** we know that $k$ divide $\phi \displaystyle\bigg( \prod_{\substack{p \leq q \\\text{p prime}}} p \bigg) = \prod_{\substack{p \leq q \\\text{p prime}}} (p - 1)$

**Many thanks for any help**

**Edit 20/09/2020 :** The sequence is added here : https://oeis.org/A333992