I found the formula to match the first for (I think so) all the numbers "not similar in value":



A : Lmit Max

[TEX]\frac{\sqrt{2178 * (p1*p2)}}{22,5} = N_{max} [/TEX] [TEX]\sim = N_{max}*\sqrt{\frac{(p1*p2)}{22,5}} = N2_{max} [/TEX](work with numbers not similar value)

B : Limit Min

[TEX]\frac{\sqrt{2178 * ((p1*p2)-9…9)}}{22,5} = N_{min}[/TEX] [TEX]\sim = N_{min}*\sqrt{\frac{(p1*p2)-9…9}{22,5}} = N2_{min}[/TEX](work with number not similar value)


[B][U][I]Example :[/I][/U][/B]


997+3 = 1000
997 * 3 = 2991

A: Limit Max

[TEX]\frac{\sqrt{2178 * (2991)}}{22,5} = 113 \sim = 113*\sqrt{\frac{2991}{22,5}} = 1302 [/TEX](work with number not similar value)

B: Limit Min

[TEX]\frac{\sqrt{2178 * ((2991)-999))}}{22,5} = 92 \sim = 92*\sqrt{\frac{(2991-999)}{22,5}} = 865[/TEX] ( work with number not similar value)

[QUOTE=Godzilla;441226]
[B][U][I]Example :[/I][/U][/B]


997+3 = 1000
997 * 3 = 2991

A: Limit Max

[TEX]\frac{\sqrt{2178 * (2991)}}{22,5} = 113 \sim = 113*\sqrt{\frac{2991}{22,5}} = 1302 [/TEX](work with number not similar value)

B: Limit Min

[TEX]\frac{\sqrt{2178 * ((2991)-999))}}{22,5} = 92 \sim = 92*\sqrt{\frac{(2991-999)}{22,5}} = 865[/TEX] ( work with number not similar value)[/QUOTE]

1) that's a range not a value and
2) have you tried to take the AGM ( arithmetic-geometric mean) it gives 1083 ( when floored) in PARI/GP
which is much closer than either of the values given. edit:in fact the geometric mean is closer still being defined as the product of those two numbers square-rooted. of course you can also square root the known product and get that they must have a pivot around roughly 17. edit: in essence what you are trying to do is define double the arithmetic mean of the two factors using the square of their geometric mean. aka 2*(a+b)/2 =a+b in terms of sqrt(a*b)^2 = a*b maybe read this ? [url]http://math.stackexchange.com/questions/829212/is-it-possible-to-calculate-the-arithmetic-mean-from-the-geometric-mean[/url]

doh should have double checked my math: sqrt(997*3) not sqrt(97*3) the point is in theory if a formula existed to do this there'd be a formula to translate arithmetic mean and geometric mean which can't happen as a sum of n numbers can be represented in multiple ways with n numbers and so you'd be saying they all have the same geometric mean which wouldn't work:

ex.

(3+3)/2 = (4+2)/2 = (5+1)/2=3 but sqrt(3*3)=sqrt(9)=3; sqrt(4*2)=sqrt(8); and sqrt(5*1)=sqrt(5) and only one of these is rational.

edit: okay bad example even number which means for one of the values it exactly equals as (n+n)/2 = 2n/2 = n and sqrt(n*n) = sqrt(n^2)=n

[QUOTE=science_man_88;441230] of course you can also square root the known product and get that they must have a pivot around roughly 17. [/QUOTE]



It's true they must have a pivot around 17-17.5 .

My latest formula work only with one factor equal to 3 and the other bigger.

[QUOTE=Godzilla;441301]My latest formula work only with one factor equal to 3 and the other bigger.[/QUOTE]

Does it show that one factor is 3 and the other factor is n/3?

[QUOTE=CRGreathouse;441315]Does it show that one factor is 3 and the other factor is n/3?[/QUOTE]


I think there must be, a scale, for factors like 1-1000, 1-10000 or similar, and more about . The last formula is trivial, but it works (--the range--), if a factor is equal to 3, have not tested it with very large numbers.

[QUOTE=Godzilla;441324]I think there must be, a scale, for factors like 1-1000, 1-10000 or similar, and more about . The last formula is trivial, but it works (--the range--), if a factor is equal to 3, have not tested it with very large numbers.[/QUOTE]

So if n has a factor in the range 1 to 1000 then you know there's a factor in n/1000 to n, if n has a factor in the range 1 to 10000 then you know there's a factor in n/10000 to n, etc.?

I have only three formula for the Sum (range Limit Min , Max ) , (that i know ) :



Formula Number 1 for factors with similar value :


[TEX]\frac{\sqrt{2178*(p1*p2)}}{22,5} [/TEX] [TEX]= Limit_{max}[/TEX]


and


[TEX]\frac{\sqrt{2178*((p1*p2)-9...9))}}{22,5}[/TEX] [TEX]= Limit_{min}[/TEX]


Formula Number 2 with 17,5 :



[TEX]\frac{\sqrt{2178*(p1*p2)}}{17,5} [/TEX] [TEX]= Limit_{max}[/TEX]


and


[TEX]\frac{\sqrt{2178*((p1*p2)-9...9))}}{17,5}[/TEX] [TEX]= Limit_{min}[/TEX]



Formula Number 3 for factors with not similar value (but not work with big number) :



[TEX] p1 * p2 = N \sim Limit_{min} = \frac {N}{4} , Limit_{max} = \frac{N}{2} [/TEX]



I want to catch it

[QUOTE=CRGreathouse;441341]So if n has a factor in the range 1 to 1000 then you know there's a factor in n/1000 to n, if n has a factor in the range 1 to 10000 then you know there's a factor in n/10000 to n, etc.?[/QUOTE]




Also :

[TEX]997 * 19 = 18943 , \frac{18943}{29} = 653 and \frac{18943}{14.5} = 1306 \sim 29(653) = Limit_{min} , 14.5(1306)= Limit_{max}[/TEX]


so


[TEX]911 * 179 = 163069 , \frac{163069}{200} = 815 and \frac{163069}{100} = 1630 \sim 200(815) = Limit_{min} , 100(1630) = Limit_{max}[/TEX]

but , how i do it ?

[QUOTE=Godzilla;441390]but , how i do it ?[/QUOTE]
Here's how. You stop posting gibberish and get a good introductory text book.

Off Topic About thread closed recently of Yeisson Acevedo.


[SPOILER] I have tested my formula, with Mersenne number, the calculations are very special, judging you.

[TEX] \frac{\sqrt{2178 * (2^{(2^{1}-1)}-1)}}{17.5} = 1,8857142857142857\sqrt{2} \sim = 2,666802717617836 [/TEX] Note [TEX] \sqrt{2}[/TEX]

and

[TEX] \frac{\sqrt{2178 * (2^{(2^{2}-1)}-1)}}{17.5} = 1,8857142857142857\sqrt{14} \sim = 7,055696786488004 [/TEX] Note [TEX] \sqrt{14}[/TEX]

and

[TEX] \frac{\sqrt{2178 * (2^{(2^{3}-1)}-1)}}{17.5} = 1,8857142857142857\sqrt{254} \sim = 30,05334033524597 [/TEX] Note [TEX] \sqrt{254}[/TEX]

and

[TEX] \frac{\sqrt{2178 * (2^{(2^{7}-1)}-1)}}{17.5} = 0,057142857142857143\sqrt{370567497576901986711614947493195582273406} \sim = 3,478528882470944E19 [/TEX] Note [TEX] \sqrt{370567497576901986711614947493195582273406}[/TEX]


Now the four root [TEX] \frac{2}{2} = 1 \sim \frac{14}{2} = 7 \sim \frac{254}{2} = 127 \sim \frac{370567497576901986711614947493195582273406}{2} = 185283748788450993355807473746597791136703[/TEX]but it isn't prime numer[/SPOILER]