M2769313 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	43.1106	68.1159%	2700000	84000000	0.7984	7.0716%	43.9091	70.3706%	2.2547%
PrimeNet	2⁵⁹	0.0277	62.7119%	12000	220000	0.0026	2.8561%	0.0303	63.7768%	1.0650%
GPU72	2⁶³	0.5763	65.0794%	15000	240000	0.0031	1.7462%	0.5794	65.6891%	0.6098%
Difference	+6	+42.5343	+3.0366%	+2685000	+83760000	+0.7954	+5.3254%	+43.3297	+4.6815%	+4.6815%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2769313	446172862974472807666529	24	78.562	80556597064772528 2⁴ × 7 × 71 × 271 × 37381390309	2021-07-29	271	37381390309	41,665	228.09	426.01

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%
2010-11-10T11:27:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.175%
2010-11-30T20:56:00	markr	tiny	110000	2365000		-		-	-	0.026	-	-	2.316%
2016-08-13T16:52:45	Jocelyn Larouche	Manual testing	142000	4730000	6	-		-	-	0.044	-	-	2.847%
2016-10-27T01:50:43	Jocelyn Larouche	low 4M	170400	170400		-		-	-	0.019	-	-	0.988%
2016-12-24T02:28:26	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.089%
2017-02-14T14:09:33	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.072%
2017-02-25T21:08:02	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	2.875%

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	-	-
2009-01-29T06:42:00	Sturle Sunde	gollumilla.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-09T15:34:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-10T10:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.354	-	-
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		-	-	2.698	-	-
2017-10-12T12:41:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.397	-	-
2019-02-23T00:52:21	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.79	-	-
2021-05-31T09:33:59	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	21.59	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.817 GHz-days
Estimated T-Level:	21.786

Digits	B1	Curves	Complete	FacMiss
20	11000	100 / 100	1.000	36.603%
25	50000	100 / 280	0.357	69.923%

New Calculation Method

Total ECM effort:	10.817 GHz-days
Estimated T-Level:	21.786

Digits	B1	Complete	FacMiss
20	11000	3.260	3.838%
25	50000	0.294	74.555%
30	250000	0.018	98.211%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		7	0.417
50000	5000000		99	10.30
50000	5000000	446172862974472807666529	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-14T22:16:00	Lupo	yorick	50000	5000000						3	0.312
2010-09-25T01:10:00	unconnected	xp-xxx	50000	5000000						3	0.312
2013-03-06T17:36:00	Donna Noble	PH2x6	50000	5000000						3	0.312
2015-03-14T16:48:00	Jason U	Server7	50000	5000000						3	0.312
2016-02-15T04:46:32	Sintax	cloud	50000	5000000						3	0.312
2016-05-20T16:38:29	Jason U	Server7	50000	5000000						3	0.312
2017-01-25T18:20:01	Marius Zens	KBWR_TV3	50000	5000000						3	0.312
2017-08-01T12:59:50	AnthonyRais	Win10Test	50000	5000000						3	0.312
2018-01-05T08:33:52	Sebastian Hornbostel	V2	50000	5000000						3	0.312
2018-10-12T02:44:44	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-07T05:41:30	Nesowa	6700T	50000	5000000						3	0.312
2020-08-15T19:44:44	GAN	XPS	50000	5000000						3	0.312
2020-09-10T06:56:52	GAN	OSB-02	50000	5000000						7	0.728
2020-10-11T11:34:48	tottenhoff	4-of-4-Ryzen-5-3600	50000	5000000						7	0.728
2020-11-09T16:30:33	nordi	sweet16	50000	5000000						7	0.728
2020-12-14T14:57:41	Denis Porva	Yrok	50000	5000000						7	0.728
2021-01-15T20:31:45	Zenzoma	AMD3970X	50000	5000000						7	0.728
2021-02-15T03:29:36	RIHATEC	i7-3770K	50000	5000000						7	0.728
2021-03-16T16:10:43	daveward2005	Dave2	50000	5000000						7	0.728
2021-04-26T11:42:25	RIHATEC	i7-3770K	50000	5000000						7	0.728
2021-06-13T13:44:57	EICCEZP	spectre	50000	50000						7	0.417
2021-06-20T09:31:08	daveward2005	MW	50000	5000000						7	0.728
2021-07-29T22:33:58	daveward2005	d12436	50000	5000000	446172862974472807666529	78.562	1	2	2903279824590069	1	0.104

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	378F3DC89D9A0CA3	0.214
2018-08-20T23:25:10	kkmrkkblmbrbk	old	378F3DC89D9A0CA3	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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

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