For me, I would say that I would feel like I would be holding things up if I tried to stake out any significant range of a large job.

I'm getting just over 2.5 million relations a day on a c164 with 8 (out of 10) cores running on the job, and I shudder to think what my output would be on something larger.

[QUOTE=xilman;281929]Why does the next one need to be GNFS? Why not SNFS up in the kilobit range, where there are many candidates?

The only answer I can see at the moment is that it gives a chance to stress-test Jason's polynomial finding code.[/QUOTE]

NFS@home is very happily doing large SNFS jobs, with I think significantly more resources than the forum can offer (apart of course from Bruce's enormous capacity), so organising more such work by hand feels redundant to me.

The polynomial-finding code has been worked on a lot recently; getting the parameters right for larger numbers is probably not completely uninteresting.

[QUOTE=bdodson;281883](By contrast, factoring a wanted Cunningham number with a known ecm pre-test has some suspense. Three prime factors? A near-miss for ecm ... & etc.)[/QUOTE]
Factoring the C187 from [URL="http://www.mersenneforum.org/showthread.php?t=13003"]this thread[/URL] would have even more suspense; not only is it unknown what sizes the factors are, but there's also a message to recover.

[QUOTE=jasonp;281896]Modern standards for RSA keys require the factors of the modulus to have the exact same number of bits. If the modulus has p-bit primes, each prime must be larger than sqrt(2)*2^(p-1)[/QUOTE]
Second try. (Please ignore the first!) Magma has a function RandomPrime.
I checked a few and got
[code]
p2=6795865632092182381090554801611929751291254620153213141853637792040419908863678815206226270618836356620243
p3=8425088594444363083756584497069027163097594304627681595990294439570195850206502157856636064495940696446767 [/code]
An online converter reports both have 106-digits, 352-bits. Next, Maple reports
[code]
evalf(sqrt(2))*2^351;

0.6486993694*10^106 [/code]
which seems to be Canadian for 6.4e105, so both p2 and p3 are in Jason's
range. No reason RSA-704 couldn't be equally modern. By contrast, our
most famous factorization, RSA-129, at p64*p65 = 3.49e63*3.27e64 definitely
isn't modern. -Bruce

Or 2^1755+1 and 2^1755-1 (C183 and C209) which the Links to factoring projects thread says would assist a result about base-2 pseudoprimes. But I don't know how significant the result is (the math's beyond me but that's a weak condition).

Chris K

[QUOTE=debrouxl;281922]For instance, TI Nspire calculators, use 1024-bit RSA signing keys on 2007-2010 models, and have already switched to 2048-bit RSA signing keys on the 2011 models. It's not desirable that other manufacturers of devices which users should be able to control, follow suit...[/QUOTE]
But it is rather inspiring (pun intended) to see people in the TI forums grappling with understanding why they have no chance to do what they want by breaking calculator crypto first. Several of them have already resolved to come up with new factorization algorithms :)

chris2be8: I thought of the Wieferich primes as well, when reading the topic for the first time :smile:
GNFS 183 is quite a bit easier than GNFS 197, while GNFS 209 is quite a bit harder.

jasonp: yeah, once in a while, someone doesn't have the orders of magnitude in their heads, but usually stops working soon enough after someone tells them.

Lest anyone think I was being disparaging, I'm sincerely not; it's a pleasure to see people discover math in their way, then figure out how it works.

[QUOTE=jasonp;281964]But it is rather inspiring (pun intended) to see people in the TI forums grappling with understanding why they have no chance to do what they want by breaking calculator crypto first. Several of them have already resolved to come up with new factorization algorithms :)[/QUOTE]

Could you kindly post here the link to the thread on that forum?

Try [url="http://www.omnimaga.org/index.php?topic=3821.0"]here[/url], [url="http://www.omnimaga.org/index.php?topic=3639.0"]here[/url], [url="http://www.omnimaga.org/index.php?topic=6810.0"]here[/url], [url="http://www.omnimaga.org/index.php?topic=8707"]here[/url] and [url="http://www.unitedti.org/forum/index.php?showtopic=9557"]here[/url] (it's a popular topic). Lionel can point to others that I missed.

Heh, jasonp kept a better track of the topic links than I did :smile:
Note that I intentionally never posted links to those topics on MersenneForum, so as to protect both the guilty, and the hopes-dasher (myself) from their wrath.

But we may be venturing into somewhat off-topic territory... mentioning the adventures of some people in the TI community was not my intention when posting about RSA-210 and RSA-704 :smile: