20220602, 13:04  #1 
May 2022
25_{8} Posts 
About M1277
[NEWCOMER ALERT]
I was messing around in mersenne.ca and saw that M1277 was the smallest composite number with no factor, and all of TF, P1 and ECM had been done to a high degree. Is it likely that we will factor M1277 in the next, say, 510 years? what about 20 years? 
20220602, 14:44  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,483 Posts 
Quote:
I would be surprised if it takes 20 years. 

20220602, 14:52  #3 
Jun 2015
Vallejo, CA/.
2·5·113 Posts 
Less than 350 digits . 10 +/ years is my guess.

20220602, 15:24  #4 
Random Account
Aug 2009
Not U. + S.A.
2^{2}·7·83 Posts 
A lot of people have done a lot of work on M1277. More than likely, far more than what has been turned in to the network servers. Some ran ECM stage 1 with Prime95 and stage 2 with GMPECM. I tried it myself probably three or four years ago. It was an extremely slow process. Even increasing the trial factoring by one bit was going to take weeks.
My guess about time: More than five years. Perhaps 10. The hardware does not exist yet and neither does the programming. I have no idea what that might look like. 
20220602, 17:19  #5  
"Curtis"
Feb 2005
Riverside, CA
12537_{8} Posts 
Quote:
For those merely curious about scale rather than details, a sieve process might need 6080GB of ram to run and the matrix might need a 1TB ram machine for the CADO matrix solving style, or a cluster totaling 11.5TB ram if using msieve for the matrix. SNFS jobs such as 2^12771 double in CPUyears difficulty roughly every 30 bits, so this job would take ~8 times longer than 2^1190 (a size that has been factored already by the CADO team). Last fiddled with by VBCurtis on 20220602 at 17:19 

20220602, 17:44  #6 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·13·191 Posts 

20220602, 17:51  #7 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,483 Posts 
Way beyond plausible ECM, though as noted above, within range of current SNFS.
Assuming a 1/3  2/3rd split, which is close to an optimal assumption absent any further information, the smaller factor would be around 130 digits. Current record is well under 100 digits. 
20220602, 17:54  #8  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,483 Posts 
Quote:
You don't need to hold all the primes and sieve array in RAM if what you want to do is determine yields. Performance would be pathetic, but so what? 

20220602, 22:02  #9 
Apr 2020
1527_{8} Posts 
M1277 (SNFS 385) is very roughly 4 times as difficult as RSA250 (GNFS 250), which took the CADO team 2700 CPUyears. So we're looking at about 10,000 CPUyears for M1277.
The hardware definitely exists. As for software, current CADO can probably handle it, but there's an upper limit of 2^31 for factor base primes, and this might add an extra thousand CPUyears or so. The CADO team have been working on extending the limit to 2^32 for a while. 
20220603, 00:05  #10 
Jun 2015
Vallejo, CA/.
2·5·113 Posts 
I stand corrected! Damn my dyslexia! I had it as 1+348. Rather than 1 +384
Last fiddled with by rudy235 on 20220603 at 00:39 Reason: dYslexia. 
20220603, 00:36  #11 
If I May
"Chris Halsall"
Sep 2002
Barbados
2×3^{3}×197 Posts 
Just between you and me (and everyone else reading this), it is OK to be dyslexic. Almost all are, but just don't yet realize it.
Being "on the spectrum" is actually nominal. Very few people are actually "normal". It took me a very long time to figure this out. Sincerely. Last fiddled with by chalsall on 20220603 at 00:37 
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