M2828887 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	21.0701	67.6471%	5000000	200000000	1.7498	9.1671%	22.8199	70.6129%	2.9658%
PrimeNet	2⁵⁹	0.0271	62.7119%	12000	240000	0.0027	2.9325%	0.0299	63.8053%	1.0935%
GPU72	2⁶³	0.5642	65.0794%	16000	260000	0.0033	1.8264%	0.5675	65.7172%	0.6378%
Difference	+5	+20.5059	+2.5677%	+4984000	+199740000	+1.7465	+7.3407%	+22.2524	+4.8957%	+4.8957%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2828887	556118813689650222982567007	27	88.846	98292864594741716969 419753 × 234168343275073	2021-03-21	419753	234168343275073	37,262,956	1,428,814	2,668,627

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%
2016-09-19T01:31:06	Jocelyn Larouche	low 4M	120000	3300000	6	-		-	-	0.033	-	-	2.866%
2016-09-21T12:09:20	Jocelyn Larouche	low 4M	120000	3630000		-		-	-	0.035	-	-	2.927%
2016-09-22T12:02:48	Jocelyn Larouche	low 4M	120000	3993000		-		-	-	0.037	-	-	2.988%
2016-12-16T01:22:15	Jocelyn Larouche	low 4M	172800	172800		-		-	-	0.019	-	-	1.142%
2016-12-24T02:28:29	Jocelyn Larouche	low 4M	207360	207360		-		-	-	0.023	-	-	1.255%
2017-02-25T21:08:04	Jocelyn Larouche	low 4M	298598	2985980	6	-		-	-	0.050	-	-	3.228%
2017-10-07T21:35:20	Jocelyn Larouche	low 4M	597196	5971960	6	-		-	-	0.100	-	-	4.096%
2019-11-10T16:24:56	masser	Manual testing	3000000	30000000	12	-		-	-	0.501	-	-	6.484%
2020-01-24T15:13:26	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.167%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-14T00:23:00	Sturle Sunde	gigi.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-13T23:34:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.347	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.694	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.321	-	-
2016-02-13T14:46:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.642	-	-
2017-10-28T16:39:40	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.283	-	-
2019-01-04T01:17:00	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.57	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.355 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:	8.355 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		65	6.783
50000	5000000	556118813689650222982567007	7	0.730
50000	6750000		7	0.841

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-20T05:02:00	James Hintz	18_060209	50000	5000000						3	0.313
2010-10-31T14:43:00	ECK	vista	50000	5000000						3	0.313
2013-06-05T20:01:00	Smurgs	Praca	50000	5000000						3	0.313
2015-04-01T01:17:00	Jason U	Server7	50000	5000000						3	0.313
2016-02-18T11:24:52	Sintax	cloud	50000	5000000						3	0.313
2016-06-10T03:14:23	lettp	Home	50000	5000000						3	0.313
2017-02-27T17:02:25	Bruce	eleven	50000	5000000						3	0.313
2017-09-10T00:49:28	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2018-03-09T01:25:45	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2019-01-17T21:08:00	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2020-09-14T09:48:19	mnd9	libproj	50000	5000000						7	0.730
2020-10-13T18:23:24	J.R. Allen	lapasus	50000	5000000						7	0.730
2020-12-17T06:09:53	lycorn	colab_A_1	50000	5000000						7	0.730
2021-01-10T17:17:16	lycorn	colab_ES	50000	6750000						7	0.841
2021-01-20T10:32:23	Zenzoma	AMD3970X	50000	5000000						7	0.730
2021-02-19T09:50:31	daveward2005	Davy	50000	5000000						7	0.730
2021-03-21T00:53:13	mnd9	l2lounge	50000	5000000	556118813689650222982567007	88.846	7	2	1200186804929627	7	0.730

date	userid	compid	res64	spent (GHz-days)
1999-12-23T00:00:00	akohler	v4_computers	2A8866F3FE864390	0.218
2018-09-09T19:35:25	kkmrkkblmbrbk	old	2A8866F3FE864390	0.218

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 = 3000000, B2 = 30000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 597196, B2 = 5971960 (P-1 stage 2)

B1 = 597196 (P-1 stage 1)

B1 = 298598, B2 = 2985980 (P-1 stage 2)

B1 = 120000, B2 = 3993000 (P-1 stage 2)

B1 = 120000, B2 = 3630000 (P-1 stage 2)

B1 = 298598 (P-1 stage 1)

B1 = 120000, B2 = 3300000 (P-1 stage 2)

B1 = 207360 (P-1 stage 1)

B1 = 172800 (P-1 stage 1)

B1 = 120000 (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

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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