M2768767 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	21.5276	67.6471%	2700000	84000000	0.7984	7.6819%	22.3260	70.1324%	2.4853%
PrimeNet	2⁵⁹	0.0277	62.7119%	12000	220000	0.0026	2.8560%	0.0303	63.7768%	1.0649%
GPU72	2⁶³	0.5764	65.0794%	15000	240000	0.0031	1.7461%	0.5795	65.6891%	0.6098%
Difference	+5	+20.9512	+2.5677%	+2685000	+83760000	+0.7954	+5.9358%	+21.7465	+4.4433%	+4.4433%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2768767	2526003416020061077623361	25	81.063	456160344301283040 2⁵ × 3² × 5 × 13711 × 23103932381	2021-04-24	13711	23103932381	349,161	140.97	263.30

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.242%
2010-11-10T11:27:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.210%
2010-12-01T02:41:00	markr	tiny	110000	2365000		-		-	-	0.026	-	-	2.606%
2016-08-12T14:59:55	Jocelyn Larouche	Manual testing	142000	4730000	6	-		-	-	0.044	-	-	3.186%
2016-10-27T01:50:43	Jocelyn Larouche	low 4M	170400	170400		-		-	-	0.019	-	-	1.129%
2016-12-24T02:28:26	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.241%
2017-02-11T04:19:48	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.682%
2017-02-25T21:08:02	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	3.203%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:21	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-01-29T00:26:00	Sturle Sunde	gollumilla.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-10T13:29:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-10T10:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.355	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.709	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.349	-	-
2016-02-08T11:13:51	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.699	-	-
2017-10-12T12:41:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.398	-	-
2019-02-23T00:52:21	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.80	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.359 GHz-days
Estimated T-Level:	4.500

Digits	B1	Curves	Complete	FacMiss
20	11000	90 / 100	0.900	40.473%
25	50000	90 / 280	0.321	72.470%

New Calculation Method

Total ECM effort:	9.359 GHz-days
Estimated T-Level:	4.500

Digits	B1	Complete	FacMiss
20	11000	2.903	5.485%
25	50000	0.262	76.921%
30	250000	0.016	98.397%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		85	8.840
50000	5000000	2526003416020061077623361	5	0.520

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-15T07:45:00	oodaira	Win02	50000	5000000						3	0.312
2010-09-21T05:24:00	James Hintz	ryan	50000	5000000						3	0.312
2013-03-07T04:08:00	Donna Noble	opt4820	50000	5000000						3	0.312
2015-03-14T05:49:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-14T18:47:45	Sintax	cloud	50000	5000000						3	0.312
2016-05-20T06:45:20	Jason U	Server7	50000	5000000						3	0.312
2017-01-20T04:27:19	Bruce	eleven	50000	5000000						3	0.312
2017-08-01T04:48:37	AnthonyRais	Win10Test	50000	5000000						3	0.312
2018-01-05T08:33:45	Sebastian Hornbostel	V2	50000	5000000						3	0.312
2018-10-11T02:50:33	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-06T22:58:45	GAN	LMS-08	50000	5000000						3	0.312
2020-08-16T23:34:41	GAN	KL-SCH05	50000	5000000						3	0.312
2020-09-10T08:45:51	GAN	AC-KL	50000	5000000						7	0.728
2020-10-10T23:58:22	MarkS	desktop-i7	50000	5000000						7	0.728
2020-11-08T04:16:55	lycorn	colab_ES_1	50000	5000000						7	0.728
2020-12-14T20:10:03	Keysarecool	Boat_Anchor	50000	5000000						7	0.728
2021-01-15T08:50:03	Zenzoma	AMD3970X	50000	5000000						7	0.728
2021-02-14T15:17:26	LordJulius	Babybox	50000	5000000						7	0.728
2021-03-15T13:11:35	daveward2005	Dave2	50000	5000000						7	0.728
2021-04-24T04:55:09	daveward2005	Dave2	50000	5000000	2526003416020061077623361	81.063	5	2	3219910906788732	5	0.520

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	209112E30219CDAB	0.214
2018-08-20T17:38:55	kkmrkkblmbrbk	old	209112E30219CDAB	0.214

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 294451, B2 = 2944510 (P-1 stage 2)

B1 = 142000, B2 = 4730000 (P-1 stage 2)

B1 = 294451 (P-1 stage 1)

B1 = 110000, B2 = 2365000 (P-1 stage 2)

B1 = 204480 (P-1 stage 1)

B1 = 170400 (P-1 stage 1)

B1 = 142000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

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