Science:Math Exam Resources/Courses/MATH312/December 2012/Question 02 (c)/Hint 1

Recall that 7 passes Miller's test if

$7^d\equiv 1mod25$

or the following holds for some r

$7^{2^{r}d}\equiv -1mod25$

where $25-1=24=2^{s}d$ for $s=3$ and $d=3$, and $0\le r\le s-1$.

If 7 passes the test, then 25 is a probable prime. If it fails the test, then the number is not prime.