what is the actual real-world application of prime numbers? Or is it just a math concept that’s neat to see and figure out but doesn’t have any actual use case?

Question

I read that they have some uses within online encryption, but to be honest I never really thought about why we learned them in school until this morning.

In: 20

Answer 1

Lets say you want to make a gear, You have a dividing head with a 40:1 gear reduction(40 turns of the knob = 1 turn of the workpiece), and there are plates that let you divide one turn of the knob by the number of holes around a circle. If you want to make a 40 tooth gear, you turn the knob 1 full rotation between each gear tooth you cut.

Lets say you’re making a clock that lists what day of the week it is, and need a 168 tooth gear. How much do you turn the crank between each cut?

Prime factorization is useful here, 168 ends in an even number, so it’s divisible by two. 84 is still divisible by 2, 42 is still divisible by 2, 21 is 3 * 7.
So we need 2 * 2 * 2 * 3 * 7 divisions.

we have 2 * 2 * 2 * 5 from the 40:1 gear reduction. We’re missing 3 and 7, so we need a plate with a 21 hole pattern in it(or some multiple thereof). Now we have that leftover 5, so we only use every fifth hole in the plate to rotate the gear the correct amount for the next cut.