What was the answer to the broken eggs POW 1 problem in high school?

The answer is that the farmer had 301 eggs to begin with.

See the first link for how someone explained it.

I got that the first possibility is 7x43 = 301, but other possible answers are

7x103 = 721

7x163 = 1141

7x223 = 1561

7x283 = 1981

7x343(first composite factor here) = 2401

7x403 (second one, 13x31) = 2821

Conjecture: all solutions are 7x(43 + 60n) for n = 0, 1, 2, 3 . . .