Formubla-bla-bla to calculate the sum of two Prime numbers just by knowing the product - Page 8

Godzilla · 2016-09-13, 22:15

Quote:

Originally Posted by science_man_88

okay well based on this going back to the huge number in post 2 has a smallest factor near: ...

Code:

  %22 = 40445364023527381951378636564391212010397122822120720357
<999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999)/17.5
%23 = 4.2326886774241279797411942169097598446 E308
<289912154831438167899885040445364023527381951378636564391212010397122822120720357/9 E308)/17.5
%24 = 1.4110247948887228971825699932010487318 E154

%24 = 1.4110247948887228971825699932010487318 E154

EDIT

<999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999))/17.5
%1 = 4.2330743846661686915477099796031461955 E231 near it
(00:30) gp >

Do you know the smallest factor ? Is It near ?

science_man_88 · 2016-09-13, 23:07

Quote:

Originally Posted by Godzilla

Code:

  %22 = 40445364023527381951378636564391212010397122822120720357
<999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999)/17.5
%23 = 4.2326886774241279797411942169097598446 E308
<289912154831438167899885040445364023527381951378636564391212010397122822120720357/9 E308)/17.5
%24 = 1.4110247948887228971825699932010487318 E154

%24 = 1.4110247948887228971825699932010487318 E154

EDIT

<999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999))/17.5
%1 = 4.2330743846661686915477099796031461955 E231 near it
(00:30) gp >

Do you know the smallest factor ? Is It near ?

my result from your method gave the same digits but with the equivalent of about 80 digits fewer. and no I don't know the factors I'm one of the typically stupid ones around here.

Godzilla · 2016-09-13, 23:20

Quote:

Originally Posted by science_man_88

my result from your method gave the same digits but with the equivalent of about 80 digits fewer. and no I don't know the factors I'm one of the typically stupid ones around here.

But i must test It with \frac22

science_man_88 · 2016-09-13, 23:25

Quote:

Originally Posted by Godzilla

But i must test It with \frac22

no I used 17.5 maybe I didn't copy it correctly I'll try it again. edit: tried it again got the same result length with what could fool me for the same digits.

Godzilla · 2016-09-13, 23:53

Quote:

Originally Posted by science_man_88

no I used 17.5 maybe I didn't copy it correctly I'll try it again. edit: tried it again got the same result length with what could fool me for the same digits.

Perhaps It work only with the numbers One very big and One very small ,i think . Because i have see a thing , the First formula in the previews post (17,5) start at 13 *3 the second step is 19*5 and so on 101*23 ; 1001*205 ; 10001*2055 ;100001*20375 and step by step Always plus. So the numbers have a proportion. But i don t understand the cicle

Godzilla · 2016-09-19, 05:40

I have found out one thing. So to find the prime factor smaller than a product .

is very simple and similar to the others . Three steps :

1) $1997 * 16257 = 32465229$

$\frac{\sqrt{2178*(32465229-9999999)}}{22} = 10054,…$ I take only four digits (1005) and not the last (never the last)

2)

$\frac{\sqrt{2178*(324652290-99999999)}}{22} = 31795,…$ I take only four digits (3179) and not the last (never the last) , and i added a zero and a 9

3)

subtract step 2 with step 1

$3179-1005 = 2174$ result is near $1997$

retina · 2016-09-19, 05:58

Quote:

Originally Posted by Godzilla

$3179-1005 = 2174$ result is near $1997$

But still wrong. There set of numbers that your formula produces wrong answers for is infinite.

Godzilla · 2016-10-17, 06:03

I have to mention them with French mathematicians, it said that, be able to improve the formula so :

$2\sqrt{product}$ if the numbers are similar

Thread : http://www.les-mathematiques.net/pho....php?5,1334720

science_man_88 · 2016-10-17, 12:00

Quote:

Originally Posted by Godzilla

I have to mention them with French mathematicians, it said that, be able to improve the formula so :

$2\sqrt{product}$ if the numbers are similar

Thread : http://www.les-mathematiques.net/pho....php?5,1334720

well yeah for example if they are the same we have p*p =p^2 for the product and 2*sqrt(p^2) =p+p for the sum. so in a prime square situation this is completely accurate. and if they are both one away from a number q we get that (q-1)(q+1)=q^2+q-q-1 = q^2-1 as the product and the sum is 2q we get just under that for using the sqrt method. in fact this can be extended to any prime power p^n by $n\sqrt[n]{product} = n(\text{geometric mean of the values}).$

Godzilla · 2016-11-04, 22:20

Quote:

Originally Posted by science_man_88

well yeah for example if they are the same we have p*p =p^2 for the product and 2*sqrt(p^2) =p+p for the sum. so in a prime square situation this is completely accurate. and if they are both one away from a number q we get that (q-1)(q+1)=q^2+q-q-1 = q^2-1 as the product and the sum is 2q we get just under that for using the sqrt method. in fact this can be extended to any prime power p^n by $n\sqrt[n]{product} = n(\text{geometric mean of the values}).$

Test it please :

$p1 * p2 = n$

$\frac{n}{22*(n2+1)} = n3 (if n3 = 22,.. stop)$

$\frac{n2}{2} = n4$ near p1 or p2

example :

$997 * 991 = 988027$

$\frac{988027}{22*2000} = 22,45..$

$\frac{2000}{2} = 1000$ is near 997 or 991

other example :

$997 * 13 = 12961$

$\frac{12961}{22*26}= 22,65..$

$\frac{26}{2} = 13$ is equal p2

work , is a possibility ?

science_man_88 · 2016-11-04, 22:39

Quote:

Originally Posted by Godzilla

Test it please :

$p1 * p2 = n$

$\frac{n}{22*(n2+1)} = n3 (if n3 = 22,.. stop)$

$\frac{n2}{2} = n4$ near p1 or p2

example :

$997 * 991 = 988027$

$\frac{988027}{22*2000} = 22,45..$

$\frac{2000}{2} = 1000$ is near 997 or 991

other example :

$997 * 13 = 12961$

$\frac{12961}{22*26}= 22,65..$

$\frac{26}{2} = 13$ is equal p2

work , is a possibility ?

I don't even know how to interpret this you don't show how to get n2 etc.

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2016-09-19, 05:40	#83
Godzilla May 2016 2·3⁴ Posts	I have found out one thing. So to find the prime factor smaller than a product . is very simple and similar to the others . Three steps : 1) $1997 * 16257 = 32465229$ $\frac{\sqrt{2178(32465229-9999999)}}{22} = 10054,…$ I take only four digits (1005) and not the last (never the last) 2) $\frac{\sqrt{2178(324652290-99999999)}}{22} = 31795,…$ I take only four digits (3179) and not the last (never the last) , and i added a zero and a 9 3) subtract step 2 with step 1 $3179-1005 = 2174$ result is near $1997$

2016-10-17, 06:03	#85
Godzilla May 2016 A2₁₆ Posts	I have to mention them with French mathematicians, it said that, be able to improve the formula so : $2\sqrt{product}$ if the numbers are similar Thread : http://www.les-mathematiques.net/pho....php?5,1334720