M2761027 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	2⁶⁹	43.2400	68.1159%	2700000	84000000	0.7984	7.0694%	44.0384	70.3700%	2.2540%
PrimeNet	2⁵⁹	0.0278	62.7119%	12000	220000	0.0026	2.8545%	0.0304	63.7763%	1.0644%
GPU72	2⁶³	0.5781	65.0794%	15000	240000	0.0031	1.7452%	0.5811	65.6888%	0.6094%
Difference	+6	+42.6619	+3.0366%	+2685000	+83760000	+0.7954	+5.3242%	+43.4573	+4.6812%	+4.6812%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2761027	8456844061560190750591	22	72.841	1531467106544085 3 × 5 × 102097807102939	2021-12-16	5	102097807102939	642.19	622,965	1,163,526

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	-	-	0.195%
2010-12-04T05:10:00	markr	tiny	110000	2365000		-		-	-	0.026	-	-	2.315%
2016-08-07T04:57:24	Jocelyn Larouche	Manual testing	142000	4730000	6	-		-	-	0.044	-	-	2.846%
2016-12-24T02:28:24	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.088%
2017-01-13T13:55:15	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.069%
2017-02-25T21:08:00	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	2.874%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:21	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-31T10:45:00	Sturle Sunde	bruckner.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-03-18T23:00:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-10T10:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.356	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.711	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.353	-	-
2016-02-08T11:13:49	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.707	-	-
2017-10-09T09:26:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.413	-	-
2019-02-21T01:08:07	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.83	-	-
2021-06-14T11:22:54	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	21.65	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.058 GHz-days
Estimated T-Level:	22.071

Digits	B1	Curves	Complete	FacMiss
20	11000	116 / 100	1.160	31.166%
25	50000	116 / 280	0.414	66.032%

New Calculation Method

Total ECM effort:	12.058 GHz-days
Estimated T-Level:	22.071

Digits	B1	Complete	FacMiss
20	11000	3.742	2.371%
25	50000	0.338	71.306%
30	250000	0.021	97.939%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		114	11.85
50000	5000000	8456844061560190750591	2	0.208

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-14T10:27:00	Smurgs	Praca	50000	5000000						3	0.312
2010-09-14T14:10:00	James Classen	towerofart	50000	5000000						3	0.312
2013-03-03T12:40:00	Donna Noble	PH2x6	50000	5000000						3	0.312
2015-03-11T20:40:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-14T03:04:25	Sintax	cloud2	50000	5000000						3	0.312
2016-05-16T07:13:14	lettp	Home	50000	5000000						3	0.312
2017-01-13T17:39:57	Bruce	eleven	50000	5000000						3	0.312
2017-07-28T10:33:05	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.312
2017-12-31T05:25:06	Angel Pescador		50000	5000000						3	0.312
2018-10-04T03:02:05	Dextronix	Dex	50000	5000000						3	0.312
2020-08-05T07:05:05	nordi	sweet16	50000	5000000						3	0.312
2020-08-12T20:50:18	GAN	LMS-02	50000	5000000						3	0.312
2020-09-06T21:49:57	Nesowa	entropy_generator_2	50000	5000000						7	0.728
2020-10-06T04:03:31	mnd9	75204b	50000	5000000						7	0.728
2020-10-31T22:44:25	daveward2005	Dave2	50000	5000000						7	0.728
2020-12-06T01:55:53	Zenzoma	AM3700X_1	50000	5000000						7	0.728
2021-01-10T06:29:46	MarkS	desktop-i7	50000	5000000						29	3.014
2021-06-14T14:15:38	daveward2005	Dave2	50000	5000000						7	0.728
2021-07-26T03:27:05	daveward2005	d12436	50000	5000000						7	0.728
2021-09-21T12:48:59	mnd9	office2	50000	5000000						7	0.728
2021-12-16T10:55:29	daveward2005	d12436	50000	5000000	8456844061560190750591	72.841	2	2	394556309229356	2	0.208

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	A0F7915E1BAF54C0	0.213
2018-08-17T20:47:48	kkmrkkblmbrbk	old	A0F7915E1BAF54C0	0.213

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 = 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