Number Properties: Chapter 4, question 1

[dakinemon]

1. How many prices are there from 10 to 41, inclusive?


The answer states:

9: The primes from 10 to 41, inclusive are: 11, 13, 17, 19, 23, 29, 31, 37, and 41


Is there any way to answer this question except for memorizing this list of prime numbers?

[StaceyKoprince]

I assume the question is supposed to say how many primes, not how many prices... :)

You can either memorize the primes or check numbers to determine whether they're prime (which takes a lot longer). You should have primes memorized at least up to 30 (well, 29 technically), and ideally up to more like 50 (er, 53).

Here's how to test a number. First, we'll assume it isn't even, because... yeah, any even number greater than 2 isn't prime. Let's say I give you a number like 83.
Is it divisible by:
3? No (8+3 = 11 and 11 isn't div. by 3)
4? No
5? No
(skip 6, b/c if it isn't div. by 2 and 3, it isn't going to be div. by 6)
7? 70, 77, 84... no
8? 80, 88... no
9? 9*9 = 81, so no. And now I can stop b/c if I get bigger than 9 (say, 11), then the second number is going to be smaller than 9, and I've already tested the smaller numbers the first time around (above).

So 83 is indeed prime.