Caution: numbers that feel prime may be divisible by 3

Caution: numbers that feel prime may be divisible by 3. For example, 51 and 57.

Conversely, numbers that feel divisible by 3 may be prime. For example, 61, 89 and 97.

Nominations for least prime-feeling numbers that actually are prime: 89 and 101.

Nominations for best prime number: 2 and 101.

Both have digits that sum to 2.

Yes, I was trying to count sheep last night.