Consider some even integer number $n$.
Let: $$C = \{c_i|i - n \mod i\}_{i=2..n}$$
For example for $n = 50$:
$c_2 = 2 - 50 \mod 2 = 2$
$c_3 = 3 - 50 \mod 3 = 1$
$c_4 = 4 - 50 \mod 4 = 2$
$c_5 = 5 - 50 \mod 5 = 5$
...
Let $C_{\text{odd}} = \{c \mid c \in C,\text{c is odd}\}$ and $C_{\text{even}} = \{c\mid c \in C,\text{c is even}\}$
Question: Is it true that number $p = n + x$ where:
- $x$ - minimal odd integer number that is not contained in the set $C_{odd}$
- $n+x < n^2$
is minimum prime number greater than $n$?
Numerical results shows that it is true up to $10^6$.