Thread: Prime counting function View Single Post
2018-02-27, 21:37   #3
Steve One

Feb 2018

3610 Posts

Quote:
 Originally Posted by CRGreathouse Let me see if I understand. You're trying to estimate the number of primes in an interval which is a below (30n + 1)^2, and your estimate is that if the interval has length L, there are about $L\prod_{7\le p\le 30n+1}\frac{p-1}{p}$ primes. Is this right?
Thank you for your reply.
I wish l could say yes or no to what you wrote, but sorry, l do not know mathematical notation so if you will allow l shall write in plain language and maybe you will be able to tell me if that is what l am saying.
I am saying that on the number line (1 + n30) 1, 31, 61, 91, 121 etc there are 210 prime numbers up to 121squared. This is calculated by a simple procedure that uses only lowest prime factors to negate primality. Prime(1) is 7. Prime(2) is 11 etc. The equation used is:

(Prime(1)minus 1)/Prime(1) × (Prime(2)minus 1)/Prime(2) × (Prime(3)minus 1)/Prime(3).....×(Prime(n)minus 1)/Prime(n) finally × (Prime(n)minus 1)/30

Prime(n) is the highest prime up to, in my example 121, which is 113.
The reason that l said there were more primes on the other number lines 7+n30, 11+n30 etc is that being that l am only using lowest prime factors to negate primality; on number line 23+n30 for example, 113 as a lowest prime factor multiplies with 131 which is greater than 121squared, therefore it allows for more primes on that line up to 121squared.
If it were that the results l got were mere coincidence, the results would not continue to be correct, as they are. Please check higher numbers for proof. It would be like a broken clock, only correct once.
As l said, l don't know mathematical notation, have never in my life studied or spoken maths with anyone. I just like playing with numbers trying to get results. If you can show an error in my reasoning, l have no problem in accepting that. In fact l would be appreciative. But my only interest is in getting results and if the results l get match reality, then l personally count that as success. My ugly writing can be tidied up if correct. Disgarded if not. Again l thank you for at least not dismissing out of hand what l wrote. I am truly interested if you can show an error. Beauty lies in the content, not the style. Please look at my twin prime proof to see if you can find an error there. With great respect, there isn't one.
If l have missed any explanation please keep up your non-combative tone.