Primality of Second Smallest Divisor

  • Divisors of \(2\) in increasing order: \(1, {\color{green} 2}\). The second divisor is a prime.

  • Divisors of \(3\) in increasing order: \(1, {\color{green} 3}\). The second divisor is a prime.

  • Divisors of \(4\) in increasing order: \(1, {\color{green} 2}, 4\). The second divisor is a prime.

What can we say about the following CONJECTURE supported by the three observations above?

The second smallest divisor of a positive integer \(n>1\) is a prime number.

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