M2110753 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	28.2387	67.6471%	2500000	125000000	0.8746	7.9024%	29.1133	70.2037%	2.5566%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6803%	0.0198	63.0856%	1.0167%
GPU72	2⁶²	0.2911	64.5161%	10000	140000	0.0016	1.4528%	0.2927	65.0316%	0.5155%
Difference	+6	+27.9476	+3.1309%	+2490000	+124860000	+0.8730	+6.4495%	+28.8206	+5.1721%	+5.1721%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2110753	2804457756856360535687	22	71.248	664326369986531 7 × 199 × 3469 × 137475743	2020-10-09	3469	137475743	265.29	0.7144	1.3337

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.224%
2009-08-02T07:18:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.878%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.352%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.511%
2011-01-25T21:32:00	James Heinrich	Q6600	140000	3010000		-		-	-	0.028	-	-	2.768%
2016-07-19T03:39:19	Jocelyn Larouche	Manual testing	186340	6020000	12	-		-	-	0.048	-	-	3.383%
2016-11-08T17:01:23	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.241%
2017-05-31T03:38:56	Jocelyn Larouche	low 4M	372680	3726800	6	-		-	-	0.053	-	-	3.362%
2017-06-10T03:57:34	Jocelyn Larouche	low 4M	447216	4472160	6	-		-	-	0.064	-	-	3.584%
2017-07-22T11:14:16	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.902%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
1999-09-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T18:38:00	Sturle Sunde	ghia.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-30T16:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2013-09-05T08:28:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.465	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.930	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.770	-	-
2015-12-27T16:49:18	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.540	-	-
2016-10-05T13:07:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.081	-	-
2019-05-13T13:38:21	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.16	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.889 GHz-days
Estimated T-Level:	22.250

Digits	B1	Curves	Complete	FacMiss
20	11000	126 / 100	1.260	28.186%
25	50000	126 / 280	0.450	63.711%

New Calculation Method

Total ECM effort:	10.889 GHz-days
Estimated T-Level:	22.250

Digits	B1	Complete	FacMiss
20	11000	4.088	1.678%
25	50000	0.371	69.034%
30	250000	0.023	97.736%
35	1000000	0.001	99.895%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		124	10.56
50000	5000000	2804457756856360535687	1	0.085
76620	24176890		1	0.245

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-28T15:39:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.255
2009-11-11T16:46:00	Samoflan	Parker	50000	5000000						3	0.255
2011-06-26T13:24:00	S36049	Wolle5	50000	5000000						3	0.255
2013-04-16T07:40:00	hiems	Laptop	50000	5000000						3	0.255
2014-11-06T22:19:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.255
2015-08-03T20:56:00	guru	w1	50000	5000000						3	0.255
2016-02-21T16:40:05	arnaud	CHAMOT09	50000	5000000						3	0.255
2016-05-30T04:48:44	Bruce	Desk6	50000	5000000						3	0.255
2016-08-19T03:57:10	Bruce	test	50000	5000000						3	0.255
2017-02-15T18:06:57	Bruce	Desk6	50000	5000000						3	0.255
2017-09-01T03:35:21	Bruce	Desk6	50000	5000000						3	0.255
2018-01-15T05:56:20	Bruce	Desk6	50000	5000000						3	0.255
2018-06-23T05:10:49	Bruce	Desk6	50000	5000000						3	0.255
2019-06-08T15:21:01	zar	eng1	50000	5000000						3	0.255
2020-01-12T04:50:07	Sergey Nosov	TS140-02	50000	5000000						3	0.255
2020-01-19T18:21:26	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-02-02T11:58:26	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-02-11T09:17:19	Keysarecool	i9	50000	5000000						3	0.255
2020-02-18T01:59:22	Nesowa	entropy_generator_2	50000	5000000						3	0.255
2020-02-25T07:23:34	Nesowa	6700T	50000	5000000						3	0.255
2020-03-03T04:21:14	ANONYMOUS	PC017	50000	5000000						3	0.255
2020-03-09T21:49:39	Sergey Nosov	TS140-02	50000	5000000						3	0.255
2020-03-11T09:39:28	ANONYMOUS	Manual testing	50000	5000000						3	0.255
2020-03-25T05:43:07	MarkS	laptop64	50000	5000000						3	0.255
2020-03-25T15:03:38	mnd9	221Rb	50000	5000000						3	0.255
2020-04-08T19:02:15	kracker	O0	50000	5000000						3	0.255
2020-04-21T18:00:53	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-04-29T09:45:03	MarkS	desktop-i7	50000	5000000						3	0.255
2020-05-10T01:31:31	daveward2005	Davy	50000	5000000						3	0.255
2020-05-25T21:09:49	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.255
2020-06-12T13:03:18	Yxinity	Olga	50000	5000000						3	0.255
2020-06-27T05:45:49	IanGlencross	glenx24	50000	5000000						3	0.255
2020-07-04T09:37:59	GAN	LMS-16	50000	5000000						3	0.255
2020-07-11T02:39:24	GAN	LMS-13	50000	5000000						3	0.255
2020-07-17T08:17:30	GAN	AC-GR	50000	5000000						3	0.255
2020-07-23T03:27:09	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.255
2020-07-29T23:37:18	GAN	PG-HP	50000	5000000						3	0.255
2020-08-07T02:48:32	mnd9	f4b	50000	5000000						3	0.255
2020-08-14T17:55:41	GAN	LMS-01	50000	5000000						3	0.255
2020-09-08T01:07:57	daveward2005	Dave2	50000	5000000						7	0.596
2020-10-09T07:14:39	mnd9	75211backdoor	50000	5000000	2804457756856360535687	71.248	1	2	1132850052815179	1	0.085
2020-11-09T21:38:10	Bruno Victal	Manual testing	76620	24176890						1	0.245

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	A87C8C245E60F3ED	0.139
1999-09-30T00:00:00	ANONYMOUS	v4_computers	A87C8C245E60F3ED	0.139
2018-04-03T00:46:26	kkmrkkblmbrbk	old	A87C8C245E60F3ED	0.139

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 447216, B2 = 4472160 (P-1 stage 2)

B1 = 372680, B2 = 3726800 (P-1 stage 2)

B1 = 186340, B2 = 6020000 (P-1 stage 2)

B1 = 447216 (P-1 stage 1)

B1 = 372680 (P-1 stage 1)

B1 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 223608 (P-1 stage 1)

B1 = 186340 (P-1 stage 1)

B1 = 140000 (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

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10⁹

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