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-   -   A next big thing (https://www.mersenneforum.org/showthread.php?t=17008)

jasonp 2012-07-23 10:10

A next big thing
 
So what number is everyone going to complain about being unfactored after this one? We'll need a candidate that can support at least five years of complaining, and preferably much more.

henryzz 2012-07-23 10:43

[QUOTE=jasonp;305579]So what number is everyone going to complain about being unfactored after this one? We'll need a candidate that can support at least five years of complaining, and preferably much more.[/QUOTE]

How about M1277? After M1061 is factored it will be the smallest exponent without any factor. It is 385 digits which is hopefully large enough.
When do you guess this will be factored?

Raman 2012-07-23 10:43

[QUOTE=jasonp;305579]So what number is everyone going to [B]claim[/B] about being unfactored after this one? We'll need a candidate that can support [B]at least five years of sieving[/B], and preferably much more.[/QUOTE]

What complain? It should be replaced by "be curious". Then, I will go after [COLOR=Magenta][B]2,1123+ c338[/B][/COLOR] please! -> For supporting atleast five years of sieving :geek:

Not that curious like such as for 2,1061-c320
which going underwent sieving for one year, linear algebra for two months to be precise enough
I listed It since you asked for an opinion / a suggestion only actually
[COLOR=White][SUP]
[SUP][SUP][SUP][SUP][SUP]Much easier candidates being listed below as follows
L1277 L1279 13,269- 2,1193- 7,379± 2,929- 2,947± 2,991± 2,1117- [STRIKE]6,299- 6,298+
[/STRIKE][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP][/COLOR][SUP][SUP][SUP][SUP][SUP][SUP][STRIKE][COLOR=White] 2,1123+ L1249 3, 607+[/COLOR][/STRIKE][/SUP][/SUP][/SUP][/SUP][/SUP][/SUP]

xilman 2012-07-23 14:58

[QUOTE=jasonp;305579]So what number is everyone going to complain about being unfactored after this one? We'll need a candidate that can support at least five years of complaining, and preferably much more.[/QUOTE]Surely the answer is obvious: RSA-1024

LaurV 2012-07-23 15:50

[QUOTE=xilman;305603]Surely the answer is obvious: RSA-1024[/QUOTE]
Now to show you that I have learned my lesson from the past: M1061 was a SNFS job, but I beleive RSA numbers are not SNFS-able, so that would be a GNFS job, and it may be more complex then the previous suggested by others. Am I right? (I would prefer RSA numbers too!)

retina 2012-07-23 16:01

[QUOTE=LaurV;305608]Now to show you that I have learned my lesson from the past: M1061 was a SNFS job, but I beleive RSA numbers are not SNFS-able, so that would be a GNFS job, and it may be more complex then the previous suggested by others. Am I right? (I would prefer RSA numbers too!)[/QUOTE]Yeah, you are pretty much correct there.

But as to the suggestion for RSA-1024: It should be easy if we use LaurV's method of getting the list of all primes at around the 512-bit level. Since those RSA numbers are guaranteed to be constructed with approximately equal sized primes then half our work has already been done by eliminating all those pesky smaller primes before we even start!

Oh, and I think this hasn't been asked yet so I'll go ahead and ask on behalf of everyone else:
Are we there yet?

LaurV 2012-07-23 16:36

Hahaha! Ten points retina! (I didn't expect that!)

jasonp 2012-07-23 17:21

I thought of RSA1024, but the factorization of RSA1024 is not holding up some momentous factor table completion accomplishment or other. Of course M1061 isn't either, but its replacement needs to aspire to a higher purpose than 'all your crypto are belong to us'

xilman 2012-07-23 17:32

[QUOTE=jasonp;305620]I thought of RSA1024, but the factorization of RSA1024 is not holding up some momentous factor table completion accomplishment or other. Of course M1061 isn't either, but its replacement needs to aspire to a higher purpose than 'all your crypto are belong to us'[/QUOTE]There's serious money riding on a factorization of RSA-1024. I've a $10 bet with RDS that the first hard kilobit factorization will be completed before the end of the decade.

Think if all the bragging rights too. Kilobit RSA protects one hell of a lot of money in the Real World. Suddenly, a lot of people are going to get seriously concerned.

Paul

chalsall 2012-07-23 17:44

[QUOTE=xilman;305622]Think if all the bragging rights too.[/QUOTE]

They have better things to do than brag.

[QUOTE=xilman;305622]RSA protects one hell of a lot of money in the Real World. Suddenly, a lot of people are going to get seriously concerned.[/QUOTE]

They already are.

xilman 2012-07-23 17:50

[QUOTE=chalsall;305623]They have better things to do than brag.



They already are.[/QUOTE]And quite right too, IMAO.

RSA has passed its use-by date. There are better alternatives readily available. Unfortunately, there is also an immense retro-fitting exercise to carry out.


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