mersenneforum.org > Math Recommended TF bit levels for M(>10^8)
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 2008-10-31, 10:14 #1 NBtarheel_33     "Nathan" Jul 2008 Maryland, USA 5×223 Posts Recommended TF bit levels for M(>10^8) Hi, Wondering if anyone knows around what bit level we should TF up to for LMH-sized numbers. I think I remember seeing something like 2^72 for numbers around M100,000,000, but I'm thinking about even bigger numbers - for instance, I was looking at numbers around M867530900 ("Jenny numbers"!) - it seems like it might be wise to go almost up to 80 bits here? I recently also worked on M999999937 (biggest number PrimeNet lists), factoring up to 2^73 - that took the better part of 24 hours, but considering that the LL test timed out to almost 70 years, I guess it's worthwhile to go much higher. Where should we start P-1'ing numbers this huge?
 2008-10-31, 11:23 #2 S485122     "Jacob" Sep 2006 Brussels, Belgium 110110110012 Posts The values I have (from the sources of v24 and v25) are : Code: Bits up to Exponent 56 1 000 000 57 1 480 000 58 1 930 000 59 2 360 000 60 2 950 000 61 3 960 000 62 5 160 000 63 6 515 000 64 8 250 000 65 13 380 000 66 23 390 000 67 29 690 000 68 37 800 000 69 47 450 000 70 58 520 000 71 75 670 000 72 96 830 000 73 115 300 000 74 147 500 000 75 186 400 000 76 227 300 000 77 264 600 000 78 337 400 000 79 420 400 000 80 516 000 000 In the source code : Code: #define FAC80 516000000L #define FAC79 420400000L #define FAC78 337400000L #define FAC77 264600000L #define FAC76 227300000L #define FAC75 186400000L #define FAC74 147500000L #define FAC73 115300000L #define FAC72 96830000L #define FAC71 75670000L #define FAC70 58520000L #define FAC69 47450000L #define FAC68 37800000L #define FAC67 29690000L #define FAC66 23390000L /* These breakevens we're calculated a long time ago on unknown hardware: */ #define FAC65 13380000L #define FAC64 8250000L #define FAC63 6515000L #define FAC62 5160000L #define FAC61 3960000L #define FAC60 2950000L #define FAC59 2360000L #define FAC58 1930000L #define FAC57 1480000L #define FAC56 1000000L This would mean that exponents above 516M should be factored to 81 bits at least. Jacob
 2008-10-31, 11:50 #3 NBtarheel_33     "Nathan" Jul 2008 Maryland, USA 5×223 Posts That's just what I was looking for Thanks, Jacob. This should almost be made into a sticky, at least in the LMH forum. It makes sense that there's no information about numbers over M5xx,000,000; I believe the current version of Prime95 will not do an LL test over M596,000,000. You really gain an appreciation for just how expensive LL testing on these kinds of numbers is when you consider that weeks, or even *months* of trial factoring makes good sense. Like on M999,999,937, I took a day to get to 73, so it would be roughly 2+4+8+16+32+64+128+256 = 510 days, or just under 1 1/2 *YEARS* :surprised just on trial factoring to 81 bits (and I bet M999,999,937 ought to go out to 84 or 85 bits, really). Wow. Then again 1 1/2 years factoring is just a brief prelude to the 70-80 year LL test my computer estimated for M999,999,937. I think I'll stick with my 30M exponents for now. Thanks again for the info!
2008-11-01, 03:35   #4
jinydu

Dec 2003
Hopefully Near M48

2×3×293 Posts

Quote:
 Originally Posted by NBtarheel_33 I was looking at numbers around M867530900 ("Jenny numbers"!)
Where did that name come from?

2008-11-01, 04:10   #5
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

23·3·421 Posts

Quote:
 Originally Posted by jinydu Where did that name come from?

Jenny 867-5309

Last fiddled with by garo on 2008-11-01 at 08:02 Reason: removed link due to a virus warning. Are you sure Batalov?

 2008-11-01, 07:40 #6 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×3,203 Posts This page is virus-infected, did you know that?
2008-11-01, 09:10   #7
jinydu

Dec 2003
Hopefully Near M48

33368 Posts

Quote:
 Originally Posted by NBtarheel_33 Then again 1 1/2 years factoring is just a brief prelude to the 70-80 year LL test my computer estimated for M999,999,937. I think I'll stick with my 30M exponents for now. Thanks again for the info!
Funny. Prime95 v24.14 at least doesn't seem to give estimates beyond 30 years (it just says estimated completion time after 2038).

 2008-11-01, 09:32 #8 NBtarheel_33     "Nathan" Jul 2008 Maryland, USA 5·223 Posts LL testing time I should have elaborated on how I got 70-80 years. I used the Advanced -> Time option in Prime95 v25.7 to run several 1000 iteration tests of M999,999,937. From the average iteration time, I extrapolated out to 999,999,937 iterations requiring somewhere between 70 and 80 years. You're right that Prime95 will not display completion times beyond 2038 (actually, beyond whatever second marks the Unix time rollover - 2,147,483,647 seconds after midnight on January 1, 1970 - hint: what's the largest value that'll fit in a 32-bit integer?). If you look in prime.ini (I think), you'll see references to estimated completion times given in Unix time. WRT the link, I actually went there and watched the video, and didn't get virusized. Hope there's not now something going on in my computer that I'm not aware of...
2008-11-01, 12:38   #9
ET_
Banned

"Luigi"
Aug 2002
Team Italia

2·2,417 Posts

Quote:
 Originally Posted by jinydu Funny. Prime95 v24.14 at least doesn't seem to give estimates beyond 30 years (it just says estimated completion time after 2038).
There is a computer bug hidden for January 2038, as there was one for Y2K.

Luigi

2008-11-01, 12:46   #10
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

2×23×137 Posts

Quote:
 Originally Posted by ET_ There is a computer bug hidden for January 2038, as there was one for Y2K.
Don't forget to check out all the other potential problems also. link. My favourite one is "The year 170,141,183,460,469,231,731,687,303,715,884,105,727 problem".

Last fiddled with by retina on 2008-11-01 at 12:46

2008-11-01, 17:04   #11
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

100111011110002 Posts

Quote:
 Originally Posted by Batalov This page is virus-infected, did you know that?
I didn't until later. The problem did crop up for me until about 10 pages in, on that site. Thanks Garo. I don't want to be the cause of a problem.

Last fiddled with by Uncwilly on 2008-11-01 at 17:25

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