Exercise · ZW-FERMAT-PRIMALITY-TEST-010 · ★★★ Advanced

Show with the base-2 test whether 341 is composite, or explain why it cannot detect it and which base reveals it.

Choose one option.

1. ABase 2 gives \( 2^{340} \equiv 1 \pmod{341} \) and the test concludes that 341 is prime
2. BBase 2 gives \( 2^{340} \equiv 2 \pmod{341} \), so 341 is prime
3. CBase 2 gives \( 2^{340} \equiv 0 \pmod{341} \), so 341 is composite
4. DBase 2 does not detect it, but base 3 gives \( 3^{340} \equiv 56 \pmod{341} \), which proves it is composite

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