please show c-d but it would be really awesome if you can answer a-d thanks! Fin

Question

please show c-d but it would be really awesome if you can answer a-d thanks!

Find all positive prime numbers le 100, using the following procedure: Make a list of all a epsilon Z with 2 le a le 100. Let P = 2. Cross out all multiples kP: where k > 1. Change P to the smallest integer m > P which has not been crossed out, if there is such an m, and go to step (c); otherwise stop. (Here P is a "variable" in the sense of computer programming.) Explain why the remaining numbers are precisely the set of prime numbers between 2 and 100.

Explanation / Answer

(c) Here, once you've made your list, simply cross out all even numbers, as they're all multiples of 2. remember to NOT cross out 2, since 2 is a prime number (its only factors are 1 and itself!)

(d) Now, continue this procedure with other integers.

For example, first I'd cross out:

4, 6, 8, 10 ...

Then I start with p = 3, and I'll cross out:

6, 9, 12, 15 (remember that 3 IS a prime number - DON'T cross it out!)

Then I start with 5 (4 is crossed out from p = 2), and cross out:

10, 15, 20, 25... (rememebr that 5 IS a prime number)

then 7:

49 (because 14, 21, 28, 35 have all already been crossed out), 77...

and continue

Final question: why is this the set of prime #s between 2 and 100?

Because you've crossed out all of the multiples of numbers, and all of the multiples of numbers ARE NOT PRIME. For instance, 15, 20, 25, 30, etc. are multiples of 5, and therefore are not prime.

By crossing out all such numbers, you've left yourself with a list of only the prime numbers between 2 and 100.

I hope that you found this answer useful towards your studies. It took a considerable amount of thought, time, and effort to compose, and and I'd sincerely appreciate a lifesaver rating! It would really make my day, and will allow me to continue answering your questions :)

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