Primality of Second Smallest Divisor

  • Divisors of 22 in increasing order: 1,21, {\color{#20A900} 2}. The second divisor is a prime.

  • Divisors of 33 in increasing order: 1,31, {\color{#20A900} 3}. The second divisor is a prime.

  • Divisors of 44 in increasing order: 1,2,41, {\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>1n>1 is a prime number.

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