M2803819 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	21.2585	67.6471%	6500000	669500000	4.7733	10.9417%	26.0318	71.1870%	3.5399%
PrimeNet	2⁵⁹	0.0274	62.7119%	12000	240000	0.0027	2.9278%	0.0301	63.8036%	1.0917%
GPU72	2⁶³	0.5692	65.0794%	15000	260000	0.0032	1.7902%	0.5724	65.7045%	0.6251%
Difference	+5	+20.6892	+2.5677%	+6485000	+669240000	+4.7702	+9.1515%	+25.4594	+5.4825%	+5.4825%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2803819	13799381170406323314167	23	73.547	2460818827892657 19 × 417947 × 309888049	2021-03-02	417947	309888049	773.35	1.9351	3.5315

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.243%
2010-11-12T11:44:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.211%
2010-11-20T06:23:00	markr	tiny	100000	2075000		-		-	-	0.023	-	-	2.485%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	122892	122892		-		-	-	0.014	-	-	0.946%
2015-01-26T12:23:00	Jocelyn Larouche	Manual testing	148699	148699		-		-	-	0.017	-	-	1.052%
2015-01-31T14:55:00	Jocelyn Larouche	Manual testing	179924	179924		-		-	-	0.020	-	-	1.164%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	197916	197916		-		-	-	0.022	-	-	1.223%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	217707	217707		-		-	-	0.024	-	-	1.284%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	350616	350616		-		-	-	0.039	-	-	1.615%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	424244	424244		-		-	-	0.048	-	-	1.761%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	466668	466668		-		-	-	0.052	-	-	1.836%
2015-03-02T13:10:00	Jocelyn Larouche	Manual testing	513334	513334		-		-	-	0.057	-	-	1.913%
2015-03-10T07:55:00	Jocelyn Larouche	Manual testing	564667	564667		-		-	-	0.063	-	-	1.992%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	621133	621133		-		-	-	0.070	-	-	2.073%
2015-03-29T20:50:00	Jocelyn Larouche	Manual testing	751570	751570		-		-	-	0.084	-	-	2.240%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	826727	826727		-		-	-	0.093	-	-	2.326%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	1000338	1000338		-		-	-	0.112	-	-	2.504%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	1100371	1100371		-		-	-	0.123	-	-	2.596%
2015-05-22T00:29:00	Jocelyn Larouche	Manual testing	1210408	1210408		-		-	-	0.136	-	-	2.689%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1331448	1331448		-		-	-	0.149	-	-	2.784%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1464592	1464592		-		-	-	0.164	-	-	2.881%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1611051	1611051		-		-	-	0.180	-	-	2.980%
2016-05-09T00:41:08	mognuts	Stanley	15000	135000		-		-	-	0.002	-	-	0.677%
2016-08-01T15:21:53	Jocelyn Larouche	Manual testing	1611051	3222102	6	-		-	-	0.190	-	-	3.730%
2018-10-19T12:14:49	Jocelyn Larouche	low 4M	2803819	2803819		-		-	-	0.314	-	-	3.589%
2019-11-13T13:54:37	masser	Manual testing	3000000	30000000	12	-		-	-	0.501	-	-	6.477%
2020-01-02T15:52:51	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.160%
2021-09-20T22:49:28	Dylan Delgado	laptop-ryzen73700	6500000	669500000		-	skipped known factor: 13799381170406323314167	-	-	4.773	-	-	10.942%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-02-13T20:01:00	Sturle Sunde	vancraft.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-01T09:18:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.350	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.700	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.333	-	-
2016-01-09T12:35:23	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	2.665	-	-
2017-10-24T17:48:46	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.330	-	-
2018-12-30T14:49:38	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.66	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.238 GHz-days
Estimated T-Level:	3.900

Digits	B1	Curves	Complete	FacMiss
20	11000	78 / 100	0.780	45.661%
25	50000	78 / 280	0.279	75.649%

New Calculation Method

Total ECM effort:	8.238 GHz-days
Estimated T-Level:	3.900

Digits	B1	Complete	FacMiss
20	11000	3.022	4.868%
25	50000	0.280	75.609%
30	250000	0.018	98.250%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		65	6.773
50000	5000000	13799381170406323314167	6	0.625
50000	6750000		7	0.840

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-24T08:52:00	Marzbug	Xeon	50000	5000000						3	0.313
2010-10-14T03:56:00	Lupo	yorick	50000	5000000						3	0.313
2013-04-01T17:05:00	hiems	Laptop	50000	5000000						3	0.313
2015-03-28T18:06:00	S36049	Wolle6	50000	5000000						3	0.313
2016-02-16T22:21:49	Jason U	Server7	50000	5000000						3	0.313
2016-05-30T20:18:42	lettp	Home	50000	5000000						3	0.313
2017-02-17T16:32:53	S36049	Wolle5	50000	5000000						3	0.313
2017-09-18T08:10:45	Prashant Keshvani	aquarius	50000	5000000						3	0.313
2018-02-06T08:05:50	Sebastian Hornbostel	V2	50000	5000000						3	0.313
2018-12-08T06:43:17	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2020-08-19T16:17:49	M. R. Mayer	nimbus	50000	5000000						7	0.729
2020-09-22T23:15:30	mnd9	libproj	50000	5000000						7	0.729
2020-10-22T16:46:12	Albrecht Heeffer	Ryzen5-factoring	50000	5000000						7	0.729
2020-11-26T02:37:08	debrouxl	toshiba1	50000	5000000						7	0.729
2020-12-29T14:43:35	Zenzoma	AMD3970X	50000	5000000						7	0.729
2021-01-29T09:19:18	lycorn	colab_ES_1	50000	6750000						7	0.840
2021-03-02T21:40:05	Zenzoma	AMD3970X	50000	5000000	13799381170406323314167	73.547	6	2	7118980552004218	6	0.625

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	C9443429C0BB7F63	0.217
2018-09-01T22:15:54	kkmrkkblmbrbk	old	C9443429C0BB7F63	0.217

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 = 6500000, B2 = 669500000 (P-1 stage 2)

B1 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 6500000 (P-1 stage 1)

B1 = 5000000 (P-1 stage 1)

B1 = 3000000, B2 = 30000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2803819 (P-1 stage 1)

B1 = 1611051, B2 = 3222102 (P-1 stage 2)

B1 = 1611051 (P-1 stage 1)

B1 = 1464592 (P-1 stage 1)

B1 = 1331448 (P-1 stage 1)

B1 = 1210408 (P-1 stage 1)

B1 = 1100371 (P-1 stage 1)

B1 = 1000338 (P-1 stage 1)

B1 = 826727 (P-1 stage 1)

B1 = 751570 (P-1 stage 1)

B1 = 621133 (P-1 stage 1)

B1 = 564667 (P-1 stage 1)

B1 = 513334 (P-1 stage 1)

B1 = 466668 (P-1 stage 1)

B1 = 424244 (P-1 stage 1)

B1 = 350616 (P-1 stage 1)

B1 = 217707 (P-1 stage 1)

B1 = 100000, B2 = 2075000 (P-1 stage 2)

B1 = 197916 (P-1 stage 1)

B1 = 179924 (P-1 stage 1)

B1 = 148699 (P-1 stage 1)

B1 = 122892 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 135000 (P-1 stage 2)

B1 = 15000 (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

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