mersenneforum.org I want to factorize 2^1277-1
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2021-09-24, 01:58   #34
tuckerkao

"Tucker Kao"
Jan 2020

10001100112 Posts

Quote:
 Originally Posted by LaurV Assuming we are in a case similar to M1061 (which is the most probable case, considering that there are many more large prime candidates than small prime candidates), you will need some more computers and some more lifetimes to get a factor of M1277 by ECM or P-1. The TF is totally out of discussion, you need few lifetimes to catch the point where ECM is now... This not considering a lot of "experiments" that other people run on this number, which are usually not reported to gimps. If the factor would have been some "low hanging fruit", it would have been found up to now. My bet is that the smaller factor has over 100-120 digits, most probably over 155 digits (the half of 385 is 192). I would be very happy if somebody proves me wrong by finding a factor, hehe...
Hopefully, there will be a different type of PRP-like test to run someday in the future, then check whether a specific Mersenne exponent is a semi-prime or not.

M1061 is a certified semi-prime. M1277 will most likely be a semi-prime as well.

Last fiddled with by tuckerkao on 2021-09-24 at 02:01

2021-09-24, 07:00   #35
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3×5×641 Posts

Quote:
 Originally Posted by tuckerkao M1061 is a certified semi-prime. M1277 will most likely be a semi-prime as well.
Can you show anything other than "because I think so" for that belief?
While factoring numbers of even lesser size we have routinely obtained three- and even four-way factorizations.

There is enough probabilistic theory on similar questions.
Dare you to learn if not that theory then at least (find it and) apply it and present the findings here -- something like: "given all data on current depth of factoring as a prior, we can derive probability p2 for M1277 having two prime factors, p3 for three, p4 for four, p5 for five, and of them p<something> is the highest, so M1277 will most likely be a <blah>." Can you manage that?

2021-09-24, 08:00   #36
tuckerkao

"Tucker Kao"
Jan 2020

563 Posts

Quote:
 Originally Posted by Batalov Can you show anything other than "because I think so" for that belief? While factoring numbers of even lesser size we have routinely obtained three- and even four-way factorizations.
Those exponents that have 3 or 4 factors are way easier to be found through large ECM or P-1, thus they won't stay unfactored for so many years.

For certain, there are no factors below 2^200 for M1277. If there are any, they must be above that size otherwise they'll be considered "low hanging fruits" by LaurV.

Last fiddled with by tuckerkao on 2021-09-24 at 08:01

2021-09-24, 08:13   #37
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3×5×641 Posts

Quote:
 Originally Posted by tuckerkao For certain, there are no factors below 2^200 for M1277. If there are any, they must be above that size otherwise they'll be considered "low hanging fruits" by LaurV.
Ok,let's count this for half of the first step. You established the prior.I will even grant you that there are no expected factors below 2^212 (which is 1/6th of the size)
Now what?
So far, what you have said is to your future argument sounds like what "There are ... (then silence)" is to a full sentence.

2021-09-24, 08:25   #38
tuckerkao

"Tucker Kao"
Jan 2020

563 Posts

Quote:
 Originally Posted by Batalov So far, what you have said is to your future argument sounds like what "There are ... (then silence)" is to a full sentence.
If the current human technology is able to discover the lower factor of M1061 which is merely 473.9 bits, but unable to do the same for M1277. It's extremely possible that the lower factor of M1277 is larger than that size and smaller than 638 bits.

It has been more than 9 years of the time gap, many extra GHz years have been invested in since then but without score the final harvestable fruit.

Last fiddled with by tuckerkao on 2021-09-24 at 08:28

2021-09-24, 08:46   #39
xilman
Bamboozled!

"ð’‰ºð’ŒŒð’‡·ð’†·ð’€­"
May 2003
Down not across

24×13×53 Posts

Quote:
 Originally Posted by tuckerkao If the current human technology is able to discover the lower factor of M1061 which is merely 473.9 bits, but unable to do the same for M1277. It's extremely possible that the lower factor of M1277 is larger than that size and smaller than 638 bits. It has been more than 9 years of the time gap, many extra GHz years have been invested in since then but without score the final harvestable fruit.
Certainly possible.

However, the largest factor ever found by ECM, the best currently available algorithm for findng partial factorizations is
16559819925107279963180573885975861071762981898238616724384425798932514688349020287. It was found 8 years ago by Propper and it has 274 bits.

1277/274 = 4.7.

There is plenty of room in there for five factors to exist but not yet discovered despite the intense effort used so far.

Last fiddled with by Dr Sardonicus on 2021-09-24 at 20:22 Reason: xingif topsy

 2021-09-24, 08:53 #40 tuckerkao   "Tucker Kao" Jan 2020 Head Base M168202123 56310 Posts I'm confused here. It showed F-ECM 2012-08-04 on the M1061 exponent results, who factored the 473.9 bits prime number? Last fiddled with by tuckerkao on 2021-09-24 at 08:53
2021-09-24, 09:22   #41
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3×5×641 Posts

Quote:
 Originally Posted by tuckerkao I'm confused here. It showed F-ECM 2012-08-04 on the M1061 exponent results, who factored the 473.9 bits prime number?
Indeed you are confused.
A Russian (collective pseudonymous) philosopher Prutkov's aphorism goes: "If you see a 'buffalo' sign on an elephant's cage, do not trust your eyes."

It was surely not factored with ECM, but with SNFS.
What is written on a cage is irrelevant, if you can see that it is an elephant. Not a buffalo.

Secondly, your comparison of M1061 to M1277's fate is as relevant as predicting weather on Oct.1st, 2021 using the weather from Oct.1st, 2012.

2021-09-24, 09:23   #42
Viliam Furik

"Viliam FurÃ­k"
Jul 2018
Martin, Slovakia

2×353 Posts

Quote:
 Originally Posted by tuckerkao I'm confused here. It showed F-ECM 2012-08-04 on the M1061 exponent results, who factored the 473.9 bits prime number?
xilman said it was found by Ryan Propper 8 years ago.

2021-09-24, 09:32   #43
ryanp

Jun 2012
Boulder, CO

5208 Posts

Quote:
 Originally Posted by Viliam Furik xilman said it was found by Ryan Propper 8 years ago.
Nope, I did not factor M1061. He was referring to another composite when talking about the ECM record (not even a Mersenne number).

Last fiddled with by ryanp on 2021-09-24 at 09:33 Reason: add link for people who don't know how to use Google

2021-09-24, 09:32   #44
tuckerkao

"Tucker Kao"
Jan 2020

563 Posts

Quote:
 Originally Posted by Viliam Furik xilman said it was found by Ryan Propper 8 years ago.
The lower factor of M1061 is 46817226351072265620777670675006972301618979214252832875068976303839400413682313921168154465151768472420980044715745858522803980473207943564433.

Xilman mentioned 16559819925107279963180573885975861071762981898238616724384425798932514688349020287. It was found 8 years ago by Propper and it has 274 bits.

2 different prime factors.

Last fiddled with by tuckerkao on 2021-09-24 at 09:33

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