Prime counting function
PRIME NUMBER COUNTING: Eg: Up to 91squared and 121squared on number line (1+n30): 1,31,61,91 etc.
(A) 0.455897334 × (B)276 = 125.8255664157 (C) up to 91squared (D) 0.430387657 × (E)488 = 210.0291769069 (F) up to 121 squared B = (91squared  1)/30. C = Prime numbers up to 91squared on number line (1 + n 30) 1, 31, 61, 91 etc. which = 125(C) E = (121squared  1)/30 F = Prime numbers up to 121 squared on number line (1 + n30) 1, 31, 61 etc. which = 210(F) A = (6 × 10 × 12 × 16 × 18 × 22 × 28 × 30 × 36 × 40 × 42 × 46 × 52 × 58 × 60 × 66 × 70 × 72 × 78 × 82 × 88)divided by (7 × 11 × 13 × 17 × 19 × 23 × 29 × 31 × 37 × 41 × 43 × 47 × 53 × 59 × 61 × 67 × 71 × 73 × 79 × 83 × 89) OR A = ((prime(1)  1) × (prime(2)  1)....× (prime(n)  1)) divided by ((prime(1) × prime(2)......×.prime(n)) Prime 1 is 7. Prime 2 is 11. Prime 3 is 13 etc Prime (n) in this case = 89(prime next down from 91) D = A × ((96 × 100 × 102 × 106 × 108 × 112) divided by (97 × 101 × 103 × 107 × 109 × 113)) In this case prime (n) = 113(prime next down from 121). There are more than 8 times as many primes up to 121 squared in totality because other number lines out of the possible 7+n30, 11+n30, 13+n30, 17+n30, 19+n30, 23+n30 and 29+n30, none except for above 1 + n30 use 112/113 and two don't use 108/109 which increases the number of primes on the number line. 
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
[$$]L\prod_{7\le p\le 30n+1}\frac{p1}{p}[/$$] primes. Is this right? 
[QUOTE=CRGreathouse;480968]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
[$$]L\prod_{7\le p\le 30n+1}\frac{p1}{p}[/$$] primes. Is this right?[/QUOTE] 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 noncombative tone. 
[url]https://math.illinoisstate.edu/day/courses/old/305/contentsummationnotation.html[/url] may help the OP.

Mistake made. Should read ...on number line (13+n30) for example, 113 as a lowest prime factor multiplies with 131 which is greater than 121squared, not (23+n30). AND, the last part of the equation should read...finally × (121squared minus 1)/30, not (prime(n)1)/30. Apologies, l do that too often. I don't seem to be able to edit the post.

[QUOTE=Steve One;481102]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[/QUOTE] So there are exactly 210 primes up to 121 × 121, and 121 = 6/7 × 10/11 × 12/13 × 16/17 × 18/19. Is that right? 
[QUOTE=CRGreathouse;481171]So there are exactly 210 primes up to 121 × 121, and 121 = 6/7 × 10/11 × 12/13 × 16/17 × 18/19. Is that right?[/QUOTE]
No! There are 210 prime numbers below 121squared on (1, 31, 61, 91 etc) 1+n30. 210 equals....(primes from 7 up to 121(7  113)each minus 1) multiplied together, divided by (primes 7 up to 121(7  113) multiplied together. Then multiplied by (121squared minus 1)/30. This result if true but irrelevant, and higher numbers that stiil work, need explaining away as to why such huge numbers being divided and multiplied result in numbers that match desired result. 
Sorry, I can't make any sense of what you've written. Good luck!

[QUOTE=CRGreathouse;481350]Sorry, I can't make any sense of what you've written. Good luck![/QUOTE]
The desire to not understand is probably the problem. 
[QUOTE=Steve One;481370]The desire to not understand is probably the problem.[/QUOTE]
Math has well used definitions, axioms, and notation which is easier to understand for anyone deep into math. 
[QUOTE=Steve One;481370]The desire to not understand is probably the problem.[/QUOTE]
I gave it two good tries, but you were either unable or unwilling to clarify so I called it quits. If someone else can translate what you wrote into proper mathematics I'd be happy to look it over, though. 
[QUOTE=science_man_88;481371]Math has well used definitions, axioms, and notation which is easier to understand for anyone deep into math.[/QUOTE]
Up to now with all the notation in the world, everybody has failed. I use numbers and ×, , +, ÷ and succeed. Who wins? The fact that the 'private language' brigade doesn't like it, l think is quite sad. 
[QUOTE=Steve One;481381]Up to now with all the notation in the world, everybody has failed. I use numbers and ×, , +, ÷ and succeed. Who wins? The fact that the 'private language' brigade doesn't like it, l think is quite sad.[/QUOTE]
It's not private it's notation [TEX]\prod[/TEX] is a product [TEX]\Sigma[/TEX] is a sum. If you know pedmas you know part of math language ( more generally convention). () Is used for functions and tup!es {} are for sets. Also plain language doesn't always convert well to math. Verbosity isn't a friend in communication usually. 
[QUOTE=Steve One;481330]
This result if true but irrelevant, and higher numbers that stiil work, need explaining away as to why such huge numbers being divided and multiplied result in numbers that match desired result.[/QUOTE] If you could write this in actual English, someone might be able to make sense of what you're trying to say. Typos matter, too: You said "if true but irrelevant", for instance. Your tirade against standard math language is foolish; using more English and less math notation doesn't make your ideas new, merely unclear. 
[QUOTE=Steve One;481381]Up to now with all the notation in the world, [B]everybody[/B] has failed.[/QUOTE]
Offtopic, but... Has it occurred to you that if _everybody_ has failed to understand you, then maybe the problem is not with everybody, and the problem is with how you express your ideas? 
[QUOTE=axn;481439]Offtopic, but...
Has it occurred to you that if _everybody_ has failed to understand you, then maybe the problem is not with everybody, and the problem is with how you express your ideas?[/QUOTE] This is what l do know. If l had said, "1,000,000 pounds to anyone who understands what is being said here", there would be lots of correct answers. What l wrote originally, although written in basic language, serves the purpose just fine to get the point across. The answer is correct. That is what matters! Anybody's refusal to accept substance over style is as l said, quite sad. What is difficult to understand from,.... primes from 7 up to 121(7 to 113) each minus 1), multiplied together,...divided by primes from 7 up to 121(7 to 113)...× (121squared minus1)/30,...that produces 210.02917, which is the number of primes on (1+n30) or 1, 31, 61, 91 etc. OR 6/7 × 10/11 × 12/13.......× (prime(n)minus 1)/prime(n) × (121squared minus 1)/30. Prime(n) equals prime before 121. There is NOTHING wrong at all. And if a person cannot understand what is being said, which they could but don't want to, then that is sad. 
[QUOTE=axn;481439]Offtopic, but...
Has it occurred to you that if _everybody_ has failed to understand you, then maybe the problem is not with everybody, and the problem is with how you express your ideas?[/QUOTE] It has occurred, but l know that is not true. Desire, or the lack of, is the problem. 
[QUOTE=Steve One;481456]I know that is not true. Desire, or the lack of, is the problem.[/QUOTE]
You said it. Now, reread what you just wrote slowly... 
[QUOTE=ET_;481470]You said it. Now, reread what you just wrote slowly...[/QUOTE]
Nope! Don't get what you are saying. 
[QUOTE=Steve One;481456]It has occurred, but l know that is not true. Desire, or the lack of, is the problem.[/QUOTE]
[QUOTE=ET_;481470]You said it. Now, reread what you just wrote slowly...[/QUOTE] [QUOTE=Steve One;481490]Nope! Don't get what you are saying.[/QUOTE] I don't think anyone is surprised to hear that. 
[QUOTE=Steve One;481456]It has occurred, but l know that is not true. Desire, or the lack of, is the problem.[/QUOTE]
None lack a desire for math, some may have a desire towards concise, precise, and accurate math though. Your lack of desire to put it in that form may be a hurdle. 
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