Formubla-bla-bla to calculate the sum of two Prime numbers just by knowing the product - Page 6

Godzilla · 2016-08-31, 18:48

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

A : Lmit Max

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

B : Limit Min

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

Example :

997+3 = 1000
997 * 3 = 2991

A: Limit Max

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

B: Limit Min

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

science_man_88 · 2016-08-31, 19:12

Quote:

Originally Posted by Godzilla

Example :

997+3 = 1000
997 * 3 = 2991

A: Limit Max

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

B: Limit Min

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

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 ? http://math.stackexchange.com/questi...geometric-mean

science_man_88 · 2016-08-31, 21:06

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

Godzilla · 2016-09-01, 07:38

Quote:

Originally Posted by science_man_88

of course you can also square root the known product and get that they must have a pivot around roughly 17.

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.

CRGreathouse · 2016-09-01, 12:08

Quote:

Originally Posted by Godzilla

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

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

Godzilla · 2016-09-01, 14:51

Quote:

Originally Posted by CRGreathouse

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

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.

CRGreathouse · 2016-09-01, 17:51

Quote:

Originally Posted by Godzilla

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.

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.?

Godzilla · 2016-09-02, 06:52

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

Formula Number 1 for factors with similar value :

$\frac{\sqrt{2178*(p1*p2)}}{22,5}$ $= Limit_{max}$

and

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

Formula Number 2 with 17,5 :

$\frac{\sqrt{2178*(p1*p2)}}{17,5}$ $= Limit_{max}$

and

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

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

$p1 * p2 = N \sim Limit_{min} = \frac {N}{4} , Limit_{max} = \frac{N}{2}$

I want to catch it

Godzilla · 2016-09-02, 08:27

Quote:

Originally Posted by CRGreathouse

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.?

Also :

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

so

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

but , how i do it ?

Batalov · 2016-09-02, 16:11

Quote:

Originally Posted by Godzilla

but , how i do it ?

Here's how. You stop posting gibberish and get a good introductory text book.

Godzilla · 2016-09-03, 07:29

Off Topic About thread closed recently of Yeisson Acevedo.

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

2016-08-31, 21:06	#58
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	doh should have double checked my math: sqrt(9973) not sqrt(973) 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(33)=sqrt(9)=3; sqrt(42)=sqrt(8); and sqrt(51)=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(nn) = sqrt(n^2)=n Last fiddled with by science_man_88 on 2016-08-31 at 21:24

2016-09-02, 06:52	#63
Godzilla May 2016 2×3⁴ Posts	I have only three formula for the Sum (range Limit Min , Max ) , (that i know ) : Formula Number 1 for factors with similar value : $\frac{\sqrt{2178(p1p2)}}{22,5}$ $= Limit_{max}$ and $\frac{\sqrt{2178((p1p2)-9...9))}}{22,5}$ $= Limit_{min}$ Formula Number 2 with 17,5 : $\frac{\sqrt{2178(p1p2)}}{17,5}$ $= Limit_{max}$ and $\frac{\sqrt{2178((p1p2)-9...9))}}{17,5}$ $= Limit_{min}$ Formula Number 3 for factors with not similar value (but not work with big number) : $p1 * p2 = N \sim Limit_{min} = \frac {N}{4} , Limit_{max} = \frac{N}{2}$ I want to catch it Last fiddled with by Godzilla on 2016-09-02 at 07:20

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2016-08-31, 18:48	#56
Godzilla May 2016 10100010₂ Posts	I found the formula to match the first for (I think so) all the numbers "not similar in value": A : Lmit Max $\frac{\sqrt{2178 * (p1p2)}}{22,5} = N_{max}$ $\sim = N_{max}\sqrt{\frac{(p1p2)}{22,5}} = N2_{max}$ (work with numbers not similar value) B : Limit Min $\frac{\sqrt{2178 ((p1p2)-9…9)}}{22,5} = N_{min}$ $\sim = N_{min}\sqrt{\frac{(p1p2)-9…9}{22,5}} = N2_{min}$ (work with number not similar value) Example :* 997+3 = 1000 997 * 3 = 2991 A: Limit Max $\frac{\sqrt{2178 * (2991)}}{22,5} = 113 \sim = 113\sqrt{\frac{2991}{22,5}} = 1302$ (work with number not similar value) B: Limit Min $\frac{\sqrt{2178 ((2991)-999))}}{22,5} = 92 \sim = 92*\sqrt{\frac{(2991-999)}{22,5}} = 865$ ( work with number not similar value)

2016-09-03, 07:29	#66
Godzilla May 2016 242₈ Posts	Off Topic About thread closed recently of Yeisson Acevedo. 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