Question

I'm having a problem with understanding question ps1b. I think it means that you should add the logs of all the primes that come before prime number n. Then divide the sum of the logs by n. But when I do that for 23 & 29 the ratio for 23 is higher than for 29. Here is how I would do that part on the command line:

(log(2)+log(3)+log(5)+log(7)+log(11)+log(13)+log(17)+log(19))/23

and

(log(2)+log(3)+log(5)+log(7)+log(11)+log(13)+log(17)+log(19)+log(23))/29

But the ratio for 23: 0.69946106453043633
Ratio for 29: 0.66286547241824778

What am I missing?

Answer 1

Here is a copy of my actual code:
http://dpaste.com/527780/

So in my code if you enter prime 23 and then prime 29 you will see that the ratio for 23 is lower than 29, and my understanding of the problem is that the ratio should always get greater as n gets greater.

After reading several posts here, it seems like most people solved this the same way I did. I'm beginning to think I should just move on, so let me know if you see any problems with my code please.

Answer 2

I meant to say the ratio for 23 is greater than 29.

Answer 3

"... theory that states that for sufficiently large n ...."
maybe 23 and 29 are not sufficiently large

"... the ratio of the sum of the logs of the primes to the value n slowly get closer to 1, it does not approach this limit monotonically. "

I think the second one is your answer

Answer 4

Oh, great point. I missed that about "sufficiently large." I think I'm ready to move forward. Thanks!