Prime testing

     

True or False

\(98402937\) is a prime number?

Statement

If an odd integer \(n>1\) satisfies \({ 2 }^{ n-1 }\equiv 1(mod\quad n)\), then \(n\) must be a prime?

What is the smallest number that doesn't satisfy the above statement?

When \(n = 3\), \(2^{n}-3 = 5\). This is the first value of \(n\) for which \(2^n - 3\) is prime. What is the \(24\)th value of \(n\) such that \(2^{n}-3\) is a prime number?

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