M2082503 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	57.3285	69.5652%	2500000	125000000	0.8746	7.2674%	58.2031	71.7770%	2.2118%
PrimeNet	2⁵⁸	0.0184	63.7931%	9000	160000	0.0016	2.6735%	0.0201	64.7611%	0.9680%
GPU72	2⁶²	0.2950	66.1290%	9000	140000	0.0015	1.3992%	0.2965	66.6030%	0.4739%
Difference	+7	+57.0335	+3.4362%	+2491000	+124860000	+0.8731	+5.8681%	+57.9066	+5.1741%	+5.1741%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2082503	126508758447150154511297	24	76.744	30374207971645216 2⁵ × 7 × 135599142730559	2021-12-24	32	135599142730559	11,001	704,336	1,315,503

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.179%
2009-07-26T12:31:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.751%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.297%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.435%
2011-01-24T16:22:00	James Heinrich	Q6600	135000	2936250		-		-	-	0.027	-	-	2.431%
2016-07-07T00:37:27	Jocelyn Larouche	Manual testing	182403	5872500	12	-		-	-	0.047	-	-	2.999%
2016-11-04T12:39:36	Jocelyn Larouche	low 4M	218883	218883		-		-	-	0.021	-	-	1.075%
2016-11-07T03:11:22	Jocelyn Larouche	low 4M	262659	262659		-		-	-	0.025	-	-	1.181%
2016-11-11T16:54:52	Jocelyn Larouche	low 4M	315190	315190		-		-	-	0.030	-	-	1.294%
2017-04-04T14:33:56	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.267%
2017-05-13T16:00:17	Jocelyn Larouche	low 4M	390228	3902280	6	-		-	-	0.055	-	-	3.072%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T11:30:00	Sturle Sunde	kinner.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-17T19:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.148	-	-
2013-09-02T08:36:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.471	-	-
2015-03-31T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.943	-	-
2015-03-31T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.794	-	-
2015-11-05T09:47:18	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.588	-	-
2016-09-14T10:22:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.177	-	-
2019-04-01T03:15:22	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.35	-	-
2021-08-26T09:33:33	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	28.71	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.771 GHz-days
Estimated T-Level:	23.625

Digits	B1	Curves	Complete	FacMiss
20	11000	203 / 100	2.030	13.000%
25	50000	203 / 280	0.725	48.370%

New Calculation Method

Total ECM effort:	17.771 GHz-days
Estimated T-Level:	23.625

Digits	B1	Complete	FacMiss
20	11000	6.606	0.135%
25	50000	0.597	55.038%
30	250000	0.037	96.385%
35	1000000	0.002	99.831%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		7	0.355
50000	5000000		197	16.75
50000	5000000	126508758447150154511297	5	0.425
76620	24176890		1	0.245

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-04T15:21:00	Jayson King	atlas	50000	5000000						3	0.255
2009-11-03T05:12:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.255
2011-06-06T14:25:00	Lukasz Wrobel	w-s	50000	5000000						3	0.255
2013-04-11T22:11:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-08-22T17:21:00	he4var		50000	5000000						3	0.255
2015-07-26T05:20:00	dragon325	Falken-i7-920	50000	5000000						3	0.255
2016-02-20T08:04:20	Sintax	cloud2	50000	5000000						3	0.255
2016-05-17T19:04:04	Jason U	Server7	50000	5000000						3	0.255
2016-07-26T10:43:35	Bruce	test	50000	5000000						3	0.255
2017-01-11T18:04:36	Bruce	Desk6	50000	5000000						3	0.255
2017-07-29T18:29:35	Bruce	Desk6	50000	5000000						3	0.255
2017-12-23T07:24:47	Bruce	Desk6	50000	5000000						3	0.255
2018-05-16T22:01:10	Bruce	Desk6	50000	5000000						3	0.255
2018-10-14T04:22:27	storm5510	7700_Kaby_Lake	50000	5000000						3	0.255
2020-01-07T13:10:22	Per Jessen	earth	50000	5000000						3	0.255
2020-01-10T00:32:39	Corey	Computer	50000	5000000						3	0.255
2020-01-17T09:09:09	EricP	Cannonfodder	50000	5000000						3	0.255
2020-01-22T21:31:31	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-01-30T07:01:34	daveward2005	MW	50000	5000000						3	0.255
2020-02-08T11:08:34	mnd9	kitchen	50000	5000000						3	0.255
2020-02-15T23:25:12	mnd9	office2	50000	5000000						3	0.255
2020-02-23T13:42:50	mnd9	libproj	50000	5000000						3	0.255
2020-02-29T17:50:20	EricP	Cannonfodder	50000	5000000						3	0.255
2020-03-07T04:25:35	mnd9	office2	50000	5000000						3	0.255
2020-03-15T15:16:29	ANONYMOUS		50000	5000000						3	0.255
2020-03-25T04:57:13	mnd9	office2	50000	5000000						3	0.255
2020-04-04T13:08:56	daveward2005	MW	50000	5000000						3	0.255
2020-04-18T10:33:23	Oliver Kruse	IOS-1	50000	5000000						3	0.255
2020-04-26T20:17:21	nordi	sweet16	50000	5000000						3	0.255
2020-05-06T11:06:29	Oliver Kruse	IOS-1	50000	5000000						3	0.255
2020-05-17T18:32:41	mnd9	25836b	50000	5000000						3	0.255
2020-06-05T17:17:11	IanGlencross	glenx24	50000	5000000						3	0.255
2020-06-23T05:46:09	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.255
2020-07-02T06:36:38	GAN	OSK-SEK	50000	5000000						3	0.255
2020-07-08T23:13:41	daveward2005	Davy	50000	5000000						3	0.255
2020-07-14T18:56:42	GAN	LMS-01	50000	5000000						3	0.255
2020-07-21T00:07:37	Ahmed Azhad	c5.large.az	50000	5000000						3	0.255
2020-07-27T21:40:05	GAN	KA-HP	50000	5000000						3	0.255
2020-08-05T18:31:23	Leo Custodio	GCP-013	50000	5000000						3	0.255
2020-08-12T01:28:43	rextherunt	ice	50000	5000000						3	0.255
2020-08-29T23:51:27	Sergey Nosov	TS140-02	50000	5000000						7	0.595
2020-10-02T13:11:34	mnd9	25836b	50000	5000000						7	0.595
2020-10-29T11:01:00	mnd9	libproj	50000	5000000						7	0.595
2020-11-09T21:37:29	Bruno Victal	Manual testing	76620	24176890						1	0.245
2020-12-22T04:33:09	Leo Custodio	GCP-013	50000	5000000						7	0.595
2021-01-20T05:37:05	daveward2005	Dave2	50000	5000000						7	0.595
2021-02-17T20:12:58	enoenoeno		50000	5000000						7	0.595
2021-03-20T01:13:46	Zenzoma	AMD3970X	50000	5000000						7	0.595
2021-06-18T06:34:10	Jonathan Webb	do-primes-2	50000	5000000						7	0.595
2021-07-02T22:03:32	daveward2005	d12436	50000	5000000						7	0.595
2021-07-30T11:43:53	C.D.B.	i7-6850K	50000	5000000						7	0.595
2021-09-30T19:26:19	-Anonymous-		50000	50000						7	0.355
2021-10-09T14:07:22	Cubox	Onyx	50000	5000000						7	0.595
2021-12-24T18:41:39	daveward2005	Dave2	50000	5000000	126508758447150154511297	76.744	5	2	5981809032752446	5	0.425

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	1541C839F8ED769A	0.137

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 390228, B2 = 3902280 (P-1 stage 2)

B1 = 182403, B2 = 5872500 (P-1 stage 2)

B1 = 390228 (P-1 stage 1)

B1 = 315190 (P-1 stage 1)

B1 = 135000, B2 = 2936250 (P-1 stage 2)

B1 = 262659 (P-1 stage 1)

B1 = 218883 (P-1 stage 1)

B1 = 182403 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

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10¹⁵

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