Didn't even find a useless factor of an uninteresting number! Take that! - Page 12

bsquared · 2016-01-27, 15:34

Quote:

Originally Posted by storflyt32

When I say "divide" I mean the result being returned by means of the software, which is an approximation to the result when it in fact does not do so.

In fact starting with 3, it factorizes down into a P305 which is known.

This is the key idea to focus on, I think.

To have one number "divide" another, it must do so with no remainder. So, for instance, 3 divides 12 because 12/3 = 4, with remainder 0. The operation in math that gives you the remainder is called "mod" (short for modulo). In many software packages this operation is represented by %. So, returning to the example we have that 12%3 = 0.

No small number, 3 or 7455602825647884208337395736200454918783366342657 both being "small", will divide rsa-1024. So we have that RSA1024%3 != 0.

If you insist on dividing anyway, what the software package is telling you is the result *without any remainder*. To take another small example, try 13/3. The result is still 4, but now with remainder 1. However, if you take the result "4" and multiply it with 3, you *get a different number than you started with*. 3*4 = 12. But you started with 13. Does this make sense?

This is why when you divide a number into RSA-1024 that leaves a remainder, you are no longer dealing with RSA1024 anymore.

Try out the % operator. If the result is a number that is not zero, STOP any further work - it will have nothing to do with rsa1024.

storflyt32 · 2016-01-27, 21:53

Yes, I was thinking about the % (or mod) operator earlier on today, because I found it to be possibly of quite high
interest when it comes to this.

I will check this out in the coming days.

wblipp · 2016-01-28, 00:11

Quote:

Originally Posted by storflyt32

When I say "divide" I mean the result being returned by means of the software, which is an approximation to the result when it in fact does not do so.

Could you give a trivial example? For example, what is 91 divided by 3?

storflyt32 · 2016-01-31, 11:28

Sorry, I lost the one that was trying to give me some answers.

But if I try asking it in this way instead.

RSA-512 like RSA-768 were being factorized as a result of more or less distributed projects, at least for the latter number.

In which way are you able to determine that some numbers are harder to factorize than others?

The only thing that is evident to me is that you may only be able to measure a composite number against another, which also should be larger.

Also the gcd command, which may be used to find the greatest common divisor for two different numbers.

As an example, I came across a 158 digit composite number a little while ago.

This number apparently is not easy to factorize.

Because this number is composite, it does not "divide" from RSA-1024, which is having 309 digits.

Because of that the only option is try factorizing the closest approximation of such an answer as given by the software.

Doing such a thing anyway, the answer is a C144, which next factorizes into C81 which is being worked on right now.

In fact even the C158 may not be as difficult as RSA-512 to factorize. Possibly less than half of that.

But the fact is that only looking at the number is telling about the possible complexity when it comes to factorizing such a number.

Read above and you may notice I made a comment about that.

Possibly you may be able to give me an answer.

Edit: I did not notice wblipp's question before posting. My eyes are not working well.

You are correct here. 91 / 3 is 30,3333... or trivially rounded to 30.

Honestly, I am having slight trouble understanding the mod or % command.

91 mod 3 returns 1.

91 is having factors 7 and 13.

30 is 2 * 3 * 5.

science_man_88 · 2016-01-31, 12:19

Quote:

Originally Posted by storflyt32

Honestly, I am having slight trouble understanding the mod or % command.

all it does is take remainder on division your 30.3333333333..... means 90/3 = 30 remainder 1. it's also called clock arithmetic because it is used in timekeeping every time the time is x:53 the number of minutes into the day is 53 mod 60.

storflyt32 · 2016-01-31, 13:36

Yes, but 53 mod 60 does not give me anything more or is helpful when it comes to an answer being returned.

Only 53 itself being returned back as an answer.

Next dividing 53 with 60 using Windows Calculator returns 0,883333... as the answer.

Also when flipping around 18867924528301886792452830188679 is having a P30 factor.

science_man_88 · 2016-01-31, 13:43

Quote:

Originally Posted by storflyt32

Yes, but 53 mod 60 does not give me anything more or is helpful when it comes to an answer being returned.

Only 53 itself being returned back as an answer.

Next dividing 53 with 60 using Windows Calculator returns 0,883333... as the answer.

right because 53 is 60*x+53 with x=0. but the point is say you want to know what the 293rd minute of every day is we can write 293 as 60*x+53 so the minutes into an hour is 53 how many hours are there solve for x and find its remainder when divided by 12 ( if on 12 hour time 24 if on 24 hour time).

storflyt32 · 2016-01-31, 14:47

Getting back to this a little later.

Needs some more coffee first.

The only thing noticed is that there may be things learnt from even smaller numbers, like 293.

But something else in the meantime.

(2^1153223-1)/4573105889235910801109267528278073569467723559031741597532613079

http://factordb.com/index.php?id=1000000000001153223

not prime according to isprime(ans) using Yafu.

Edit: What about the following?

>> 293 mod 60

ans = 15529

>> factor(15529)

fac: factoring 15529
fac: using pretesting plan: normal
fac: no tune info: using qs/gnfs crossover of 95 digits
div: primes less than 10000
Total factoring time = 0.0030 seconds

***factors found***

P2 = 53
P3 = 293

ans = 1

science_man_88 · 2016-01-31, 15:16

Quote:

Originally Posted by storflyt32

Edit: What about the following?

>> 293 mod 60

ans = 15529

>> factor(15529)

fac: factoring 15529
fac: using pretesting plan: normal
fac: no tune info: using qs/gnfs crossover of 95 digits
div: primes less than 10000
Total factoring time = 0.0030 seconds

***factors found***

P2 = 53
P3 = 293

ans = 1

I'm not all that familiar with YAFU or most of the programs except some math, my guess is that YAFU does the straightforward factorization for this one. edit: but you can check that it makes sense in that the remainders work as (53*53) mod 60 =49 and it's important to note it's the remainders that matter in finding that. as (a*60+b)*(c*60+d) =a*c*60^2+c*60*b+d*a*60+b*d = (a*c*60+c*b+d*a)*60+b*d so the remainder of the answer of multiplication is only dependent on the remainders of the two numbers you multiply.

storflyt32 · 2016-01-31, 16:55

Added a PRP1094 to my list right now.

storflyt32 · 2016-02-07, 10:33

Came across this thing.

http://factordb.com/index.php?id=1100000000820337198

http://factordb.com/index.php?id=1100000000820341791

By means of multiplying the numbers in this instance, should be added.

By coincidence, not that far from RSA-1024, but anyway, what am I supposed to be doing?

The C284 is probably a difficult number to factorize, but does Yafu become stuck here because of the C161, or the P123?

2016-01-27, 21:53	#123
storflyt32 Feb 2013 2×229 Posts	Yes, I was thinking about the % (or mod) operator earlier on today, because I found it to be possibly of quite high interest when it comes to this. I will check this out in the coming days. Last fiddled with by storflyt32 on 2016-01-27 at 21:54

2016-01-31, 11:28	#125
storflyt32 Feb 2013 2·229 Posts	Sorry, I lost the one that was trying to give me some answers. But if I try asking it in this way instead. RSA-512 like RSA-768 were being factorized as a result of more or less distributed projects, at least for the latter number. In which way are you able to determine that some numbers are harder to factorize than others? The only thing that is evident to me is that you may only be able to measure a composite number against another, which also should be larger. Also the gcd command, which may be used to find the greatest common divisor for two different numbers. As an example, I came across a 158 digit composite number a little while ago. This number apparently is not easy to factorize. Because this number is composite, it does not "divide" from RSA-1024, which is having 309 digits. Because of that the only option is try factorizing the closest approximation of such an answer as given by the software. Doing such a thing anyway, the answer is a C144, which next factorizes into C81 which is being worked on right now. In fact even the C158 may not be as difficult as RSA-512 to factorize. Possibly less than half of that. But the fact is that only looking at the number is telling about the possible complexity when it comes to factorizing such a number. Read above and you may notice I made a comment about that. Possibly you may be able to give me an answer. Edit: I did not notice wblipp's question before posting. My eyes are not working well. You are correct here. 91 / 3 is 30,3333... or trivially rounded to 30. Honestly, I am having slight trouble understanding the mod or % command. 91 mod 3 returns 1. 91 is having factors 7 and 13. 30 is 2 * 3 * 5. Last fiddled with by storflyt32 on 2016-01-31 at 11:39

2016-01-31, 13:36	#127
storflyt32 Feb 2013 712₈ Posts	Yes, but 53 mod 60 does not give me anything more or is helpful when it comes to an answer being returned. Only 53 itself being returned back as an answer. Next dividing 53 with 60 using Windows Calculator returns 0,883333... as the answer. Also when flipping around 18867924528301886792452830188679 is having a P30 factor. Last fiddled with by storflyt32 on 2016-01-31 at 13:44

2016-01-31, 14:47	#129
storflyt32 Feb 2013 2·229 Posts	Getting back to this a little later. Needs some more coffee first. The only thing noticed is that there may be things learnt from even smaller numbers, like 293. But something else in the meantime. (2^1153223-1)/4573105889235910801109267528278073569467723559031741597532613079 http://factordb.com/index.php?id=1000000000001153223 not prime according to isprime(ans) using Yafu. Edit: What about the following? >> 293 mod 60 ans = 15529 >> factor(15529) fac: factoring 15529 fac: using pretesting plan: normal fac: no tune info: using qs/gnfs crossover of 95 digits div: primes less than 10000 Total factoring time = 0.0030 seconds *factors found* P2 = 53 P3 = 293 ans = 1 Last fiddled with by storflyt32 on 2016-01-31 at 15:02

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2016-01-31, 16:55	#131
storflyt32 Feb 2013 111001010₂ Posts	Added a PRP1094 to my list right now.

2016-02-07, 10:33	#132
storflyt32 Feb 2013 712₈ Posts	Came across this thing. http://factordb.com/index.php?id=1100000000820337198 http://factordb.com/index.php?id=1100000000820341791 By means of multiplying the numbers in this instance, should be added. By coincidence, not that far from RSA-1024, but anyway, what am I supposed to be doing? The C284 is probably a difficult number to factorize, but does Yafu become stuck here because of the C161, or the P123?