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That's the point indeed ^^.

In the second one, you're applying your logic to half of the values the first algorithm goes by. It means that the more value you'll have to parse, the more efficient the second algorithm will be :).

I know it's checking the remainder against the square of a value instead of iterating through all the values. My question is, why does they both work similar?

Thank You!

Please look at the answer I received at Quora.

quora.com/Why-do-both-of-these-programs-behave-th…

Indu Pillai i see, and I knew that this is the answer but still the math prove is missing to me :D. the prove by induction is missing :D that's what I meant with my missing formal math education.

j :)