M2818687 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	42.3555	68.1159%	5000000	200000000	1.7498	8.4862%	44.1052	70.8217%	2.7058%
PrimeNet	2⁵⁹	0.0272	62.7119%	12000	240000	0.0027	2.9306%	0.0300	63.8046%	1.0928%
GPU72	2⁶³	0.5662	65.0794%	15000	260000	0.0032	1.7920%	0.5694	65.7051%	0.6258%
Difference	+6	+41.7892	+3.0366%	+4985000	+199740000	+1.7466	+6.6942%	+43.5358	+5.1166%	+5.1166%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2818687	329933020093104293214698249	27	88.092	58526012305215920252 2² × 43 × 2411 × 141131278889431	2021-09-18	2411	141131278889431	30,480,482	861,134	1,608,359

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	-	-	0.196%
2016-09-14T01:53:47	Jocelyn Larouche	low 4M	135048	3300000	6	-		-	-	0.034	-	-	2.612%
2016-09-21T12:09:26	Jocelyn Larouche	low 4M	135048	3630000		-		-	-	0.036	-	-	2.668%
2016-12-21T00:33:38	Jocelyn Larouche	low 4M	194468	194468		-		-	-	0.022	-	-	1.064%
2017-01-10T10:25:18	Jocelyn Larouche	low 4M	233361	233361		-		-	-	0.026	-	-	1.170%
2017-03-17T00:52:40	Jocelyn Larouche	low 4M	336039	3360390	6	-		-	-	0.056	-	-	3.029%
2018-09-03T21:22:26	Jocelyn Larouche	low 4M	499246	499246		-		-	-	0.056	-	-	1.681%
2019-06-27T13:59:16	BigBrother	Winston	1000000	30000000	12	-		-	-	0.289	-	-	5.421%
2019-09-28T03:14:01	masser	Manual testing	2818687	28186870	12	-		-	-	0.470	-	-	5.852%
2020-01-19T15:04:42	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	8.486%

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	-	-
2009-02-13T04:32:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-23T12:04:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.348	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.697	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.326	-	-
2016-02-12T10:12:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.651	-	-
2017-10-24T17:48:50	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.302	-	-
2019-01-02T03:46:01	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.60	-	-
2021-05-19T10:49:42	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	21.21	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.644 GHz-days
Estimated T-Level:	21.804

Digits	B1	Curves	Complete	FacMiss
20	11000	101 / 100	1.010	36.237%
25	50000	101 / 280	0.361	69.673%

New Calculation Method

Total ECM effort:	10.644 GHz-days
Estimated T-Level:	21.804

Digits	B1	Complete	FacMiss
20	11000	3.274	3.787%
25	50000	0.296	74.364%
30	250000	0.018	98.192%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		93	9.70
50000	5000000	329933020093104293214698249	1	0.104
50000	6750000		7	0.841

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-21T10:35:00	S36049	Wolle3	50000	5000000						3	0.313
2010-10-27T00:49:00	Donna Noble	PH2-940-v3-MVB	50000	5000000						3	0.313
2013-04-10T23:14:00	Jacques MOLNE	Old_faithfull	50000	5000000						3	0.313
2015-03-28T18:46:00	Jason U	Server7	50000	5000000						3	0.313
2016-02-18T01:04:28	Sintax	cloud	50000	5000000						3	0.313
2016-06-06T04:38:26	Jason U	Server7	50000	5000000						3	0.313
2017-02-27T01:38:05	Marius Zens	KBWR_TV3	50000	5000000						3	0.313
2017-09-04T05:26:04	Angel Pescador		50000	5000000						3	0.313
2018-07-29T16:48:20	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2018-12-28T15:08:19	Syntony	Hadfield	50000	5000000						3	0.313
2020-09-03T11:32:22	mnd9	25836b	50000	5000000						7	0.730
2020-10-07T06:51:41	GAN	XPS	50000	5000000						7	0.730
2020-11-05T02:39:30	Nesowa	entropy_generator_2	50000	5000000						7	0.730
2020-12-07T17:11:30	Zenzoma	AMD3970X	50000	5000000						7	0.730
2021-01-10T13:35:39	rextherunt	ice	50000	5000000						7	0.730
2021-02-08T13:06:56	daveward2005	Dave2	50000	5000000						7	0.730
2021-03-09T16:36:31	Zenzoma	AMD3970X	50000	5000000						7	0.730
2021-04-17T01:18:04	Chang Chia-Tche	ex-ctcpc	50000	5000000						7	0.730
2021-06-08T20:41:16	daveward2005	d12436	50000	5000000						7	0.730
2021-07-17T23:30:15	kutens	terra	50000	6750000						7	0.841
2021-09-18T05:53:17	daveward2005	Dave2	50000	5000000	329933020093104293214698249	88.092	1	2	7093994641419969	1	0.104

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	30D65A9726CCE9A8	0.218
2018-09-06T14:23:29	kkmrkkblmbrbk	old	30D65A9726CCE9A8	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 = 2818687, B2 = 28186870 (P-1 stage 2)

B1 = 2818687 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 336039, B2 = 3360390 (P-1 stage 2)

B1 = 499246 (P-1 stage 1)

B1 = 336039 (P-1 stage 1)

B1 = 135048, B2 = 3630000 (P-1 stage 2)

B1 = 135048, B2 = 3300000 (P-1 stage 2)

B1 = 233361 (P-1 stage 1)

B1 = 194468 (P-1 stage 1)

B1 = 135048 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

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10¹⁰

10¹¹

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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