Recommended TF bit levels for M(>10^8)

[NBtarheel_33]

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?

[S485122]

The values I have (from the sources of v24 and v25) are :

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 :

#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

[NBtarheel_33]

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!

[jinydu]

Originally Posted by NBtarheel_33

I was looking at numbers around M867530900 ("Jenny numbers"!)

Where did that name come from?

[Uncwilly]

Originally Posted by jinydu

Where did that name come from?

Jenny 867-5309

[Batalov]

This page is virus-infected, did you know that?

[jinydu]

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).

[NBtarheel_33]

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...

[ET_]

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

[retina]

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".

[Uncwilly]

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.