M2 834 329 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	10.4836	67.1642%	360000	287380170	1.7916	8.0024%	12.2752	69.7918%
Target	2⁶³	0.5631	65.0794%	16000	260000	0.0033	1.8271%	0.5664	65.7174%
Difference	+4	+9.9205	+2.0848%	+344000	+287120170	+1.7883	+6.1753%	+11.7088	+4.0744%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2834329	6974412546660565399	19	62.597	1230346326531 3 × 7 × 58587920311	2013-01-10	7	58587920311	0.4545	357.48	667.68
2834329	1040664114090508564583	22	69.818	183582095460779 71 × 19853 × 130240433	2023-01-31	19853	130240433	78.818	0.7968	1.4842
2834329	1127969593227878533991	22	69.934	198983532474155 5 × 11 × 13 × 2393 × 116296969	2023-01-31	2393	116296969	44.633	0.7099	1.3253

exponent	prime factors	composite factor	digits	bits*
2834329	6974412546660565399 1040664114090508564583	7258020854172245018097304770394686663617	40	132.415
2834329	6974412546660565399 1127969593227878533991	7866925283260130368841359132815299977409	40	132.531
2834329	1040664114090508564583 1127969593227878533991	1173837477457521523451688582703803784240753	43	139.752
2834329	6974412546660565399 1040664114090508564583 1127969593227878533991	81868268305201267168843712867843202405884674532418 40917505447	61	202.349

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.301%
2023-01-31	USAFSS	6917th_Scty_Sq	360000	287380170			1040664114090508564583 1127969593227878533991	43	139.752	1.792	0.438	3.583	8.002%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2013-01-10	dbaugh	Manual testing	?	?	6974412546660565399	62.597	19	0.238	0.441	0.479
2009-02-12	Sturle Sunde	gibsy.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-14	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.108	-	-

ECM factoring results:

Total ECM effort:	0.626 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.626

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-21	James Hintz	04_060209	50000	5000000						3	0.313
2010-11-04	Donna Noble	PH2-940-v3-MVB	50000	5000000						3	0.313

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Ralph Green,Jr.		428F5B94B397FC90	0.219
1999-05-16	ANONYMOUS	v4_computers	428F5B94B397FC90	0.219

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-22

Oliver Kruse

GTX-2

6974412546660565399

51D12EDF26656B__

2017-12-07

kkmrkkblmbrbk

c4.xlarge

6974412546660565399

51D12EDF26656B__

2023-02-01

LordJulius

WhiteBox

6974412546660565399

1040664114090508564583

1127969593227878533991

51D12EDF26656B86

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 360000, B2 = 287380170 (P-1 stage 2)

B1 = 360000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront