20180727, 00:00  #1 
Jun 2003
The Computer
3×131 Posts 
Factoring to 87 bits
I've been thinking that in order to revive this project a bit, it might be good to get candidates up to 87 bits, as there are currently six that are at 86 bits and according to mersenne.ca (link below) 87 is the optimal bit depth for these candidates. This will pave the way for an eventual P1 and PRP/LL test of these candidates.
https://www.mersenne.ca/factorbits.p...ent=3321930371 But please let me know if any of this is incorrect, since I'm going off what the mersenne.ca and my scant/outdated knowledge. 
20180727, 14:27  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{2}×41×61 Posts 
I am not sure that even 87 bits will eventually be considered the level that we want.
Have fun. May you slay a billion digit exponent with a factor. 
20180727, 16:11  #3  
Banned
"Luigi"
Aug 2002
Team Italia
3×1,609 Posts 
Quote:
Luigi 

20180727, 18:12  #4  
Quasi Admin Thing
May 2005
967 Posts 
Quote:
https://www.mersenne.ca/tf1G.php According to that page, wich holds records of TF bitdepth for all n>1000M to n<=2^32, the optimal bit level for TF for n=3321930371 is 91 bit. That is just how it looks now and it may very well be that these TF bit depths is subject for change in the future. But hey it is your ressources and you can do whatever you want and if you like to do n=3321930371 to 87 bits only, then thats your choice Happy hunting and TF 

20180728, 02:42  #5  
Jun 2003
The Computer
611_{8} Posts 
Thanks all for the responses.
Quote:
http://www.mersenne.ca/exponent/3321930371 Perhaps I'm misreading it, but that seems to imply that 91 would be too high, or one of the estimates is off, perhaps due to it being so far outside of normal assigned ranges. 

20180728, 06:56  #6  
Jun 2003
19·271 Posts 
Quote:
EDIT: Compare the LL GHDays for an exponent 1/10th the size: http://www.mersenne.ca/exponent/332193019. An exponent 10 times the size should be at least 100 times the effort, so 600K might actually be a conservative estimate. Last fiddled with by axn on 20180728 at 06:58 

20180802, 19:54  #7 
Jun 2003
The Computer
3·131 Posts 
Thanks axn for the explanation. I might have to wait to get a better GPU, or simply do the lower ranges.

20200823, 16:37  #8  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5,783 Posts 
Quote:
An LL test should only be considered on large exponents if an initial PRP/GEC/Proof/Cert test sequence yield a probablyprime result. LL even with Jacobi check is simply too likely to have an undetected error in such large long computations. LL confirmation would probably best be done with different software and hardware and frequent comparison of interim residues. Last fiddled with by kriesel on 20200823 at 16:46 

20200823, 17:54  #9 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
1697_{16} Posts 
If implementing R Gerbicz' method of storing numerous residues to perform a correctness check of a gigadigit LL run, I estimate 40.5MB/100Mdigit x 10 x sqrt(3,321,9xx,xxx) or 405MB x 57636 ~ 23.TB disk space needed, which is a large but feasible array.
At 10^{1.5} lower for 100Mdigit, 0.7TB is much more manageable. Last fiddled with by kriesel on 20200823 at 18:08 
20200917, 13:57  #10 
Jun 2003
The Computer
189_{16} Posts 
Thanks kriesel for the insight in the last two posts. I am interested to see if we can get a P1 or PRP test going on an exponent once we get one TFed to 91 bits. Perhaps I could be tempted to get a RTX 3090 and get it done in a semireasonable time frame!

20200918, 22:03  #11 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5,783 Posts 
I assume you're referring to the last TF with the RTX3090. Start lobbying Mihai and George now for a gigadigitcapable fft length in gpuowl, and robust error checking in P1, which I estimate would take a month to run on a Radeon VII, and start saving for a Radeon VII Pro for the PRP multiyear run.
Last fiddled with by kriesel on 20200918 at 22:34 
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