M2804519 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	2⁶⁷	10.5950	67.1642%	4000000	404000000	2.8886	10.6904%	13.4836	70.6745%	3.5103%
PrimeNet	2⁵⁹	0.0274	62.7119%	12000	240000	0.0027	2.9280%	0.0301	63.8036%	1.0918%
GPU72	2⁶³	0.5691	65.0794%	15000	260000	0.0032	1.7903%	0.5723	65.7045%	0.6252%
Difference	+4	+10.0259	+2.0848%	+3985000	+403740000	+2.8855	+8.9001%	+12.9114	+4.9699%	+4.9699%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2804519	31104719844499938057713	23	74.720	5545464274711624 2³ × 19 × 36483317596787	2015-03-23	19	36483317596787	1,737.4	222,609	415,771

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	-	-	0.301%
2010-11-12T11:44:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.253%
2010-11-20T00:10:00	markr	tiny	100000	2075000		-		-	-	0.023	-	-	2.797%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	122886	122886		-		-	-	0.014	-	-	1.086%
2015-01-26T18:12:00	Jocelyn Larouche	Manual testing	148691	148691		-		-	-	0.017	-	-	1.204%
2015-01-31T14:55:00	Jocelyn Larouche	Manual testing	179916	179916		-		-	-	0.020	-	-	1.328%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	197907	197907		-		-	-	0.022	-	-	1.393%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	217697	217697		-		-	-	0.024	-	-	1.461%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	350600	350600		-		-	-	0.039	-	-	1.824%
2015-02-13T18:03:00	Jocelyn Larouche	Manual testing	385660	385660		-		-	-	0.043	-	-	1.903%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	424226	424226		-		-	-	0.048	-	-	1.983%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	466648	466648		-		-	-	0.052	-	-	2.065%
2015-03-02T13:10:00	Jocelyn Larouche	Manual testing	513312	513312		-		-	-	0.057	-	-	2.149%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	564643	564643		-		-	-	0.063	-	-	2.235%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	621107	621107		-		-	-	0.070	-	-	2.323%
2021-09-21T19:25:56	Dylan Delgado	laptop-ryzen73700	4000000	404000000		-		-	-	2.889	-	-	10.690%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-02-14T03:13:00	Sturle Sunde	vancraft.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-02T15:15:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.350	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.251 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.251 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	0.938
50000	5000000	31104719844499938057713	3	0.313

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-19T05:59:00	SubPrime	dijkstra	50000	5000000						3	0.313
2010-10-14T22:17:00	Lupo	yorick	50000	5000000						3	0.313
2013-03-23T14:13:00	Richard Kint	xps	50000	5000000						3	0.313
2015-03-23T12:36:00	Bruce	desk16	50000	5000000	31104719844499938057713	74.720	3	2		3	0.313

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	Ethan O'Connor	v4_computers	84BA52E8AC1CA510	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 = 4000000, B2 = 404000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 621107 (P-1 stage 1)

B1 = 564643 (P-1 stage 1)

B1 = 513312 (P-1 stage 1)

B1 = 466648 (P-1 stage 1)

B1 = 424226 (P-1 stage 1)

B1 = 385660 (P-1 stage 1)

B1 = 350600 (P-1 stage 1)

B1 = 217697 (P-1 stage 1)

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

B1 = 197907 (P-1 stage 1)

B1 = 179916 (P-1 stage 1)

B1 = 148691 (P-1 stage 1)

B1 = 122886 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000 (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

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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