M2070071 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	28.7936	69.1176%	2813228	48612579	0.5061	6.8259%	29.2997	71.2257%	2.1080%
PrimeNet	2⁵⁸	0.0185	63.7931%	9000	160000	0.0016	2.6705%	0.0202	64.7600%	0.9669%
GPU72	2⁶²	0.2968	66.1290%	9000	130000	0.0015	1.3664%	0.2983	66.5918%	0.4628%
Difference	+6	+28.4969	+2.9886%	+2804228	+48482579	+0.5046	+5.4596%	+29.0015	+4.6338%	+4.6338%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2070071	78851964672922463366423	23	76.062	19045715019659341 13 × 1166441 × 1256004377	2020-04-08	1166441	1256004377	10,371	6.6291	12.185

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.222%
2009-07-31T20:56:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.874%
2010-12-26T14:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.350%
2011-01-06T23:25:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.509%
2011-01-19T11:59:00	James Heinrich	Q6600	135000	3071250		-		-	-	0.028	-	-	2.754%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	166006	166006		-		-	-	0.016	-	-	1.059%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	200866	200866		-		-	-	0.019	-	-	1.171%
2015-01-30T21:42:00	Jocelyn Larouche	Manual testing	243047	243047		-		-	-	0.023	-	-	1.290%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	294086	294086		-		-	-	0.028	-	-	1.417%
2015-02-02T07:32:00	Jocelyn Larouche	Manual testing	323494	323494		-		-	-	0.031	-	-	1.483%
2015-02-06T22:00:00	Jocelyn Larouche	Manual testing	646988	646988		-		-	-	0.062	-	-	2.017%
2015-02-20T16:56:00	Jocelyn Larouche	Manual testing	746988	746988		-		-	-	0.071	-	-	2.139%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	821686	821686		-		-	-	0.078	-	-	2.223%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	1093662	1093662		-		-	-	0.104	-	-	2.484%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	1323330	1323330		-		-	-	0.126	-	-	2.667%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	1455663	1455663		-		-	-	0.139	-	-	2.762%
2015-05-22T00:29:00	Jocelyn Larouche	Manual testing	1601229	1601229		-		-	-	0.153	-	-	2.858%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	1761351	1761351		-		-	-	0.168	-	-	2.955%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1937486	1937486		-		-	-	0.185	-	-	3.055%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	2131234	2131234		-		-	-	0.203	-	-	3.156%
2015-07-21T01:20:00	Jocelyn Larouche	Manual testing	2344357	2344357		-		-	-	0.224	-	-	3.259%
2016-03-15T22:08:57	Jocelyn Larouche	Manual testing	2813228	28132280	12	-		-	-	0.400	-	-	6.172%
2016-10-07T05:48:04	Jocelyn Larouche	low 4M	2813228	48612579	12	-		-	-	0.506	-	-	6.826%
2018-02-22T22:48:10	Jocelyn Larouche	low 4M	2823228	5646456	6	-		-	-	0.284	-	-	4.274%
2018-04-10T21:07:14	Jocelyn Larouche	low 4M	2823228	11292912	6	-		-	-	0.313	-	-	5.090%
2018-04-11T22:23:20	Jocelyn Larouche	low 4M	2823228	22585824	12	-		-	-	0.372	-	-	5.911%
2018-04-14T11:03:17	Jocelyn Larouche	low 4M	2823228	45171648	12	-		-	-	0.489	-	-	6.740%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.056	-	-
2009-01-02T18:21:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-15T07:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.148	-	-
2013-09-01T20:21:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.474	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.948	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.805	-	-
2015-11-04T09:56:23	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.610	-	-
2016-09-07T22:47:46	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.220	-	-
2019-03-28T01:31:29	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.44	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.710 GHz-days
Estimated T-Level:	3.950

Digits	B1	Curves	Complete	FacMiss
20	11000	79 / 100	0.790	45.204%
25	50000	79 / 280	0.282	75.379%

New Calculation Method

Total ECM effort:	6.710 GHz-days
Estimated T-Level:	3.950

Digits	B1	Complete	FacMiss
20	11000	2.548	7.821%
25	50000	0.230	79.428%
30	250000	0.014	98.592%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		78	6.626
50000	5000000	78851964672922463366423	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-11T09:40:00	Battlemaxx	Maxx_mom	50000	5000000						3	0.255
2009-10-29T01:56:00	James Hintz	ryan	50000	5000000						3	0.255
2011-04-27T00:44:00	Lupo	yorick	50000	5000000						3	0.255
2013-03-13T23:21:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-08-12T12:36:00	OS1	L3	50000	5000000						3	0.255
2015-07-21T01:05:00	guru	w6	50000	5000000						3	0.255
2016-02-19T17:29:08	Sintax	cloud2	50000	5000000						3	0.255
2016-05-16T19:51:15	James P McMillan	caturday	50000	5000000						3	0.255
2016-07-23T01:43:47	Bruce	test	50000	5000000						3	0.255
2016-12-31T18:32:48	Bruce	Desk6	50000	5000000						3	0.255
2017-07-16T04:34:04	Bruce	Desk6	50000	5000000						3	0.255
2017-12-13T09:01:48	Bruce	Desk6	50000	5000000						3	0.255
2018-04-30T19:02:22	Bruce	Desk6	50000	5000000						3	0.255
2018-10-11T12:44:43	storm5510	7700_Kaby_Lake	50000	5000000						3	0.255
2019-12-30T22:13:45	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-01-05T00:15:45	TheJudger	myECM	50000	5000000						3	0.255
2020-01-19T17:54:18	Bommer	6600K	50000	5000000						3	0.255
2020-01-25T08:43:06	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-02-03T05:10:49	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-02-18T06:50:05	mnd9	eileen	50000	5000000						3	0.255
2020-02-25T11:43:43	mat10243x	K2	50000	5000000						3	0.255
2020-03-03T23:29:34	kracker	O0	50000	5000000						3	0.255
2020-03-10T07:52:17	mnd9	75211backdoorb	50000	5000000						3	0.255
2020-03-14T15:35:21	mnd9	75201b	50000	5000000						3	0.255
2020-03-17T14:02:05	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-03-28T01:11:15	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-04-09T03:04:55	Keysarecool	Boat_Anchor	50000	5000000	78851964672922463366423	76.062	1	2	2093255125863273	1	0.085

date	userid	compid	res64	spent (GHz-days)
2003-09-21T00:00:00	ANONYMOUS	v4_computers	F8E2468605C42011	0.136
2015-03-28T17:59:00	MadPoo	Manual testing	F8E2468605C42011	0.136

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 = 2813228, B2 = 48612579 (P-1 stage 2)

B1 = 2823228, B2 = 45171648 (P-1 stage 2)

B1 = 2813228, B2 = 28132280 (P-1 stage 2)

B1 = 2823228, B2 = 22585824 (P-1 stage 2)

B1 = 2823228, B2 = 11292912 (P-1 stage 2)

B1 = 2823228, B2 = 5646456 (P-1 stage 2)

B1 = 2823228 (P-1 stage 1)

B1 = 2813228 (P-1 stage 1)

B1 = 2344357 (P-1 stage 1)

B1 = 2131234 (P-1 stage 1)

B1 = 1937486 (P-1 stage 1)

B1 = 1761351 (P-1 stage 1)

B1 = 1601229 (P-1 stage 1)

B1 = 1455663 (P-1 stage 1)

B1 = 1323330 (P-1 stage 1)

B1 = 1093662 (P-1 stage 1)

B1 = 821686 (P-1 stage 1)

B1 = 746988 (P-1 stage 1)

B1 = 646988 (P-1 stage 1)

B1 = 323494 (P-1 stage 1)

B1 = 135000, B2 = 3071250 (P-1 stage 2)

B1 = 294086 (P-1 stage 1)

B1 = 243047 (P-1 stage 1)

B1 = 200866 (P-1 stage 1)

B1 = 166006 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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