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Old 2018-07-27, 00:00   #1
clowns789
 
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Default 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 P-1 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But please let me know if any of this is incorrect, since I'm going off what the mersenne.ca and my scant/outdated knowledge.
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Old 2018-07-27, 14:27   #2
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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.
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Old 2018-07-27, 16:11   #3
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Quote:
Originally Posted by clowns789 View Post
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 P-1 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But please let me know if any of this is incorrect, since I'm going off what the mersenne.ca and my scant/outdated knowledge.
I'm afraid the project is not coordinated anymore... I took offline the site when we had more than six months without reservations. I don't think William is following it anymore. But if you want to offer your work to advance the bitlevel to 87, you are mostly welcome! Just post here your advancements, so that people like James at mersenne.ca can keep his records updated.

Luigi
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Old 2018-07-27, 18:12   #4
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Quote:
Originally Posted by clowns789 View Post
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 P-1 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.
Well it is at least not consistent with the bit levels shown on this subsite of mersenne.ca:

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
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Old 2018-07-28, 02:42   #5
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Thanks all for the responses.

Quote:
Originally Posted by KEP View Post
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.
Interestingly, according to the following link, factoring to 91 bits would require over 150K GHz-days of computation, while a LL test requires only 91K:

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.
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Old 2018-07-28, 06:56   #6
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Quote:
Originally Posted by clowns789 View Post
Interestingly, according to the following link, factoring to 91 bits would require over 150K GHz-days of computation, while a LL test requires only 91K:

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.
The figure of 91K is wrong. I think it is closer to 600K. James's site doesn't have P95 timing data for a FFT big enough to handle that exponent, and so uses timing from a smaller FFT, hence the discrepancy. If 87 bits is good enough for CPU TF, then 91 bits is correct for GPU TF.

EDIT:- Compare the LL GH-Days 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 2018-07-28 at 06:58
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Old 2018-08-02, 19:54   #7
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Thanks axn for the explanation. I might have to wait to get a better GPU, or simply do the lower ranges.
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