Are you happy or unhappy? (Missed me?)

Algebra Level pending

The sum of all the happy numbers from 1-100 can be expressed as * a * b * c *, where a, b, and c are prime numbers, a being the smallest number, b being the middle number, and c being the largest number. Find (b-a)^c.

For the whole set, go to this link: https://brilliant.org/profile/jonathan-ydncjm/sets/are-you-happy-or-unhappy/

This is going to be the last of the happy problems, I hope you guys had a great experience! For the last challenge, prove your answer, and generalize it, and find a formula, if you haven't already.

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