# Primality of Second Smallest Divisor

• Divisors of $2$ in increasing order: $1, {\color{#20A900} 2}$. The second divisor is a prime.

• Divisors of $3$ in increasing order: $1, {\color{#20A900} 3}$. The second divisor is a prime.

• Divisors of $4$ in increasing order: $1, {\color{#20A900} 2}, 4$. 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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