We're given a number $n\in [10^9,10^{10}]$ and its smallest prime factor $p$. Then we are asked to find $p - 1$ numbers with $a^{p-1} \equiv 1\bmod n$, and some other number of numbers which are not.
We did this by just rerunning until $p = 3$, using Sage:```K = Integers(11081914353)r = K(1)print(r.nth_root(3, all=True))
> [1, 7429528459, 7346357344, 3693971452, 41585557, 11040328795, 7387942903, 3735557008, 3652385893]```
And then submitting these, interspersing with small numbers which when cubed can never be 1 modulo $n$ (such as 2 or 3).
Given the pattern `001100`, we can do:```001100Enter: 2 3 7429528459 7346357344 4 5b'flag{pr1mes_r_pr3tty_sp3c14lll}'```