Fermat primality test

Compute. $2^4=16$, $2^5=32\equiv-3\pmod{35}$, $2^{10}\equiv9$, $2^{20}\equiv81\equiv11$, $2^{30}\equiv11\cdot9=99\equiv29\pmod{35}$, $2^{34}=2^{30}\cdot2^4\equiv29\cdot16=464\equiv464-13\cdot35=464-455=9\pmod{35}$.

Result. $2^{34}\equiv9\neq1\pmod{35}$.

Conclusion. $35$ is composite (as expected: $35=5\cdot7$).