20210924, 01:58  #34  
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{4}×47 Posts 
Quote:
M1061 is a certified semiprime. M1277 will most likely be a semiprime as well. Last fiddled with by tuckerkao on 20210924 at 02:01 

20210924, 07:00  #35  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,477 Posts 
Quote:
While factoring numbers of even lesser size we have routinely obtained three and even fourway 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 p_{2} for M1277 having two prime factors, p_{3} for three, p_{4} for four, p_{5} for five, and of them p_{<something>} is the highest, so M1277 will most likely be a <blah>." Can you manage that? 

20210924, 08:00  #36  
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{4}×47 Posts 
Quote:
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 20210924 at 08:01 

20210924, 08:13  #37  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
26B4_{16} Posts 
Quote:
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. 

20210924, 08:25  #38  
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{4}·47 Posts 
Quote:
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 20210924 at 08:28 

20210924, 08:46  #39  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2CA5_{16} Posts 
Quote:
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 20210924 at 20:22 Reason: xingif topsy 

20210924, 09:22  #41  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,477 Posts 
Quote:
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. 

20210924, 09:32  #43 
Jun 2012
Boulder, CO
3·137 Posts 
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 20210924 at 09:33 Reason: add link for people who don't know how to use Google 
20210924, 09:32  #44 
"Tucker Kao"
Jan 2020
Head Base M168202123
2^{4}×47 Posts 
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 20210924 at 09:33 
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