M2766727 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	21.5435	67.6471%	2700000	84000000	0.7984	7.6813%	22.3419	70.1322%	2.4851%
PrimeNet	2⁵⁹	0.0278	62.7119%	12000	220000	0.0026	2.8556%	0.0304	63.7767%	1.0648%
GPU72	2⁶³	0.5769	65.0794%	15000	240000	0.0031	1.7459%	0.5799	65.6890%	0.6097%
Difference	+5	+20.9666	+2.5677%	+2685000	+83760000	+0.7954	+5.9355%	+21.7620	+4.4432%	+4.4432%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2766727	88093332621952805113116559	26	86.187	15920134625127958977 3 × 5306711541709319659	2021-03-19	3	5306711541709319659	7,058,261	3.238e+10	6.048e+10

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%
2010-12-01T20:53:00	markr	tiny	110000	2365000		-		-	-	0.026	-	-	2.606%
2016-08-11T02:58:17	Jocelyn Larouche	Manual testing	142000	4730000	6	-		-	-	0.044	-	-	3.186%
2016-10-27T01:50:42	Jocelyn Larouche	low 4M	170400	170400		-		-	-	0.019	-	-	1.129%
2016-12-24T02:28:25	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.241%
2017-02-02T09:05:27	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.681%
2017-02-25T21:08:01	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	3.202%

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		-	-	0.056	-	-
2009-01-31T13:20:00	Sturle Sunde	gofy.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-03-13T03:31:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.355	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.710	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.350	-	-
2016-02-08T11:13:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.701	-	-
2017-10-12T12:41:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.402	-	-
2019-02-21T06:22:36	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.80	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.636 GHz-days
Estimated T-Level:	4.100

Digits	B1	Curves	Complete	FacMiss
20	11000	82 / 100	0.820	43.862%
25	50000	82 / 280	0.293	74.574%

New Calculation Method

Total ECM effort:	8.636 GHz-days
Estimated T-Level:	4.100

Digits	B1	Complete	FacMiss
20	11000	2.661	6.990%
25	50000	0.241	78.599%
30	250000	0.015	98.527%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		71	7.383
50000	5000000	88093332621952805113116559	4	0.416
50000	6750000		7	0.838

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-16T02:04:00	Martti Järvi	SKYNET	50000	5000000						3	0.312
2010-09-20T15:17:00	James Classen	towerofart	50000	5000000						3	0.312
2013-03-06T06:58:00	Donna Noble	opt4820	50000	5000000						3	0.312
2015-03-13T16:19:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-15T10:21:19	Jason U	Server7	50000	5000000						3	0.312
2016-05-18T17:24:24	Jason U	Server7	50000	5000000						3	0.312
2017-01-18T01:04:49	Bruce	eleven	50000	5000000						3	0.312
2017-07-31T00:23:12	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.312
2017-12-31T07:49:57	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2018-10-07T11:39:47	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-06T08:51:29	GAN	LMS-03	50000	5000000						3	0.312
2020-08-14T16:03:04	IanGlencross	glenx24	50000	5000000						3	0.312
2020-09-08T06:44:15	Chang Chia-Tche	ex-ctcpc	50000	5000000						7	0.728
2020-10-09T03:36:41	mnd9	75211backdoor	50000	5000000						7	0.728
2020-11-06T10:35:50	IanGlencross	glenx24	50000	5000000						7	0.728
2020-12-12T02:28:52	Zenzoma	AMD3970X	50000	5000000						7	0.728
2021-01-13T12:56:53	lycorn	colab_ES_1	50000	6750000						7	0.838
2021-02-18T00:43:27	mnd9	50869	50000	5000000						7	0.728
2021-03-19T04:35:53	mnd9	50869	50000	5000000	88093332621952805113116559	86.187	4	2	3216066799732880	4	0.416

date	userid	compid	res64	spent (GHz-days)
1999-09-30T00:00:00	ANONYMOUS	v4_computers	F9D704E9B1BF8CA7	0.214
2018-08-19T18:54:41	kkmrkkblmbrbk	old	F9D704E9B1BF8CA7	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 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

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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