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

[VBCurtis]

I am glad to see you use "divides" with quotations, indicating you understand that your use of the word does not have anything to do with division. This indicates you are capable of learning something.

Now, you should learn that when an attempted division has a remainder, your result is utterly useless. You seem to put quite a bit of effort into trying to factor numbers, and if you accepted that any result with a remainder should be reported to nobody (definitely not factordb) you might someday factor a number of some interest to someone.

You're an enthusiast, as are many of us on this forum. There are so many projects mentioned here that could benefit from extra effort that it's a shame your enthusiasm is wasted so completely.

[storflyt32]

Anyway, retina.

Did not forget you either.

What about the opposite way?

RSA-2048 | 2^156165461-1 ?

Not tested out, at least here, but theoretically a possibility, except for the known factor.

Has anyone tried or tested it out?

I could give it a try (for the composite number, of course).

[retina]

Originally Posted by storflyt32

Anyway, retina.

Did not forget you either.

What about the opposite way?

RSA-2048 | 2^156165461-1 ?

Not tested out, at least here, but theoretically a possibility, except for the known factor.

Has anyone tried or tested it out?

I could give it a try (for the composite number, of course).

Only if RSA2048 is of the form 2kp+1

But since we know that RSA2048 is of the form pq, then it leads to the requirement that both p and q must also be of the form 2kp+1 if we want it to divide M(156165461). Does (did) the BSAFE library allow the selection of p and q to be of the form 2kp+1 with the size of p being on the order of 156165461?

[storflyt32]

(2^57131-1)/61481396117165983261035042726614288722959856631 (PRP) (17152 digits)

FF 5127 (show) 2^17029-1<5127> = 418879343 · 4146743936...77<5118>

(2^42991-1)/(2^3307-1)/8191 (PRP) (11943 digits)

(2^63703-1)/42808417 (PRP) (19169 digits)

(2^221509-1)/292391881 (PRP)

(2^271211-1)/613961495159 (PRP)

(2^271549-1)/238749682487 (PRP)

(2^406583-1)/813167 (PRP)

FF 12422 (show) 2^41263-1<12422> = 1402943 · 983437775590306674647<21> · 1823577269...67<12395>

FF 17520 (show) 2^58199-1<17520> = 237604901713907577052391<24> · 1857215297...57<17497>

FF 19177 (show) 2^63703-1<19177> = 42808417 · 7625786008...71<19169>

FF 26001 (show) 2^86371-1<26001> = 41681512921035887<17> · 4383409247...81<25984>

FF 32027 (show) 2^106391-1<32027> = 286105171290931103<18> · 2665280850...49<32010>

FF 39267 (show) 2^130439-1<39267> = 260879 · 4316833447...53<39261>

FF 41206 (show) 2^136883-1<41206> = 536581361 · 1442981921...87<41198>

FF 52340 (show) 2^173867-1<52340> = 52536637502689<14> · 2895968516...43<52326>

CF 66681 (show) 2^221509-1<66681> = 292391881 · 2439743803...31<66673>
(Needs checking, either CF, U, or possibly PRP in my list).

U 81631 (show) (2^271211-1)/613961495159<81631> = 7211288804...33<81631>
(Needs checking, either CF, U, or possibly PRP in my list).

CF 81745 (show) 2^271549-1<81745> = 238749682487<12> · 1038364317...53<81734>
(Needs checking, either CF, U, or possibly PRP in my list).

I did not open up the last file for this right now.

The question could be about whether or not I am left to only guess when it comes to a couple of things.

At least the factorization for these numbers should be quite plain or visible here.

Perhaps rather teach me how this is supposed to be done.

The point is that I at times is supposed to rely only on a given syntax rather than be looking at a number as a whole.

Precisely that ends up being the big Sigh! here.

Just to have that fact being mentioned.

Edit:

http://factordb.com/index.php?id=1100000000853570841

This one apparently blew after three days of running.

Nothing back using the nfs command instead either.

[storflyt32]

http://factordb.com/index.php?id=1100000000854248107

http://factordb.com/index.php?id=1100000000854248837

http://factordb.com/index.php?id=1100000000822445183

In which way you prefer it, of course.

Just for fun.

[storflyt32]

http://factordb.com/index.php?id=1100000000855382007

Possibly a RSA-256 number.

Edit: Thanks, but used the wrong number first.

Getting back at it.

http://factordb.com/index.php?id=1100000000853974339

[storflyt32]

The previous post was meant to be edited for something more to be added.

I was going to mention that this number also has a PRP711 at the other end.

For now I did not note down those things that ended up getting close, but at least I have the factors and could try it out later on.

If I am not wrong, the C1133 of 2^4096+1 only has a couple of small factors in between at places now, but as mentioned, I forgot which one these were.

I guess it will be Friday again soon and if I am not late I could give it a try before then.

If we could get the answer here, it probably will break up much of the other numbers that happen to be larger in size.

[storflyt32]

http://factordb.com/index.php?id=1100000000855620070

http://factordb.com/index.php?id=1100000000855618888

http://factordb.com/index.php?id=1100000000855619562

http://factordb.com/index.php?id=1100000000855623330

[storflyt32]

http://factordb.com/index.php?id=1100000000855853314

Apparently a P28 or P29 factor here, but pressing the wrong button, when I run the number once more using Yafu,
it wants to use SIQS directly.

Either the SIQS want to finish the whole number without any intermediate results or factors, but it becomes an endless wait.

The only other alternative or option is using ecm instead, but this could probably take a day or so.

Here it probably does not work too well.

Edit: Became a P29 which was added.

[storflyt32]

http://factordb.com/index.php?id=1100000000855620070

OK if I update this one?

Yes I know that it may not be readily done, but this time it became separate factors.

[storflyt32]

http://factordb.com/index.php?id=1100000000856862335

P47 = 10788828104741394603874034857703617756401751697

P102 = 124930286153094988815617090964912266180370112196906240110381097717763649642507952667733875862772561483

Initially a PRP102

Total factoring time = 97560.6176 seconds