M2846759 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	20.9378	67.6471%	5000000	200000000	1.7498	9.1724%	22.6876	70.6146%	2.9675%
PrimeNet	2⁵⁹	0.0270	62.7119%	13000	240000	0.0028	2.9922%	0.0298	63.8276%	1.1157%
GPU72	2⁶³	0.5606	65.0794%	16000	260000	0.0033	1.8286%	0.5639	65.7179%	0.6385%
Difference	+5	+20.3772	+2.5677%	+4984000	+199740000	+1.7465	+7.3439%	+22.1237	+4.8967%	+4.8967%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2846759	2584355132932445607110953	25	81.096	453911822695993164 2² × 3 × 21961 × 1722416339177	2021-04-24	21961	1722416339177	342,723	10,510	19,629

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.244%
2008-10-31T23:37:00	Jayson King	atlas	35000	560000		-		-	-	0.007	-	-	1.388%
2011-01-25T02:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.543%
2012-01-14T20:00:00	Squeeky_Squirrel	P4_2600	195000	4875000		-		-	-	0.050	-	-	3.398%
2017-06-28T04:14:50	Jocelyn Larouche	low 4M	390000	3900000	6	-		-	-	0.065	-	-	3.554%
2019-11-01T13:51:58	masser	Manual testing	2850000	28500000	12	-		-	-	0.476	-	-	6.405%
2020-03-15T14:44:30	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.172%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:23	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-12T15:38:00	Sturle Sunde	giasha.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-05T14:31:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.108	-	-
2013-01-07T13:46:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.345	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.690	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.312	-	-
2016-02-14T20:28:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.625	-	-
2017-11-05T22:24:14	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.250	-	-
2019-01-07T01:09:16	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.50	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.364 GHz-days
Estimated T-Level:	3.950

Digits	B1	Curves	Complete	FacMiss
20	11000	79 / 100	0.790	45.204%
25	50000	79 / 280	0.282	75.379%

New Calculation Method

Total ECM effort:	8.364 GHz-days
Estimated T-Level:	3.950

Digits	B1	Complete	FacMiss
20	11000	2.564	7.700%
25	50000	0.232	79.290%
30	250000	0.014	98.580%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		69	7.208
50000	5000000	2584355132932445607110953	3	0.313
50000	6750000		7	0.842

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-22T13:36:00	James Hintz	05_060309	50000	5000000						3	0.313
2010-11-09T17:55:00	Donna Noble	ph2-940-1	50000	5000000						3	0.313
2013-04-10T23:57:00	Donna Noble	PH2x6	50000	5000000						3	0.313
2015-06-18T08:34:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.313
2015-06-18T10:14:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.313
2019-03-25T20:55:12	Claude Portenier	Petit-Idiot	50000	5000000						3	0.313
2020-07-28T17:40:31	mnd9	75204	50000	5000000						3	0.313
2020-08-05T03:33:54	GAN	LMS-03	50000	5000000						3	0.313
2020-08-13T11:49:18	daveward2005	Dave2	50000	5000000						3	0.313
2020-09-08T05:09:48	mnd9	75203b	50000	5000000						7	0.731
2020-10-09T14:55:39	LaurV	3tits	50000	5000000						7	0.731
2020-11-02T11:57:47	daveward2005	Dave2	50000	5000000						7	0.731
2020-12-07T09:54:56	Zenzoma	AMD3970X	50000	5000000						7	0.731
2021-01-09T03:32:29	Denis Porva	Yrok	50000	5000000						7	0.731
2021-02-09T07:06:02	lycorn	colab_ES_1	50000	6750000						7	0.842
2021-03-15T04:06:36	mnd9	l2lounge	50000	5000000						7	0.731
2021-04-24T04:55:01	daveward2005	Dave2	50000	5000000	2584355132932445607110953	81.096	3	2	8579368382938794	3	0.313

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	4A92388D8877FEA7	0.220
2018-09-15T13:07:14	kkmrkkblmbrbk	old	4A92388D8877FEA7	0.220

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2850000, B2 = 28500000 (P-1 stage 2)

B1 = 2850000 (P-1 stage 1)

B1 = 390000, B2 = 3900000 (P-1 stage 2)

B1 = 195000, B2 = 4875000 (P-1 stage 2)

B1 = 390000 (P-1 stage 1)

B1 = 195000 (P-1 stage 1)

B1 = 35000, B2 = 560000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 35000 (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

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10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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