M2817421 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	42.3745	68.1159%	5000000	200000000	1.7498	8.4859%	44.1243	70.8216%	2.7056%
PrimeNet	2⁵⁹	0.0273	62.7119%	12000	240000	0.0027	2.9304%	0.0300	63.8046%	1.0927%
GPU72	2⁶³	0.5665	65.0794%	15000	260000	0.0032	1.7918%	0.5697	65.7051%	0.6257%
Difference	+6	+41.8080	+3.0366%	+4985000	+199740000	+1.7466	+6.6940%	+43.5546	+5.1165%	+5.1165%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2817421	665547649852780673970143	24	79.139	118112921329964651 23 × 179 × 28689074891903	2021-06-06	179	28689074891903	53,718	175,051	326,946

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%
2016-09-13T03:53:09	Jocelyn Larouche	low 4M	135059	3300000	6	-		-	-	0.034	-	-	2.612%
2016-09-21T12:09:26	Jocelyn Larouche	low 4M	135059	3630000		-		-	-	0.036	-	-	2.668%
2016-12-21T00:33:39	Jocelyn Larouche	low 4M	194484	194484		-		-	-	0.022	-	-	1.064%
2017-01-10T10:25:18	Jocelyn Larouche	low 4M	233380	233380		-		-	-	0.026	-	-	1.170%
2017-03-17T00:52:41	Jocelyn Larouche	low 4M	336067	3360670	6	-		-	-	0.056	-	-	3.028%
2018-09-03T21:22:26	Jocelyn Larouche	low 4M	499280	499280		-		-	-	0.056	-	-	1.681%
2019-10-03T23:34:06	masser	Manual testing	2817421	28174210	12	-		-	-	0.470	-	-	5.851%
2020-01-15T14:04:59	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
1998-07-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.027	-	-
2016-02-23T16:29:22	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.027	-	-
2009-02-12T05:19:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-02-21T14:24:00	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	-	-
2016-02-12T10:12:10	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.652	-	-
2017-10-24T17:48:50	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.305	-	-
2019-01-01T23:16:49	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.61	-	-
2021-05-19T10:49:46	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	21.22	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.552 GHz-days
Estimated T-Level:	4.100

Digits	B1	Curves	Complete	FacMiss
20	11000	82 / 100	0.820	43.862%
25	50000	82 / 280	0.293	74.574%

New Calculation Method

Total ECM effort:	8.552 GHz-days
Estimated T-Level:	4.100

Digits	B1	Complete	FacMiss
20	11000	3.154	4.269%
25	50000	0.292	74.691%
30	250000	0.018	98.176%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		79	8.239
50000	5000000	665547649852780673970143	3	0.313

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-18T19:34:00	superdory		50000	5000000						3	0.313
2010-10-25T23:42:00	Donna Noble	PH2-940-v3-MVB	50000	5000000						3	0.313
2013-03-29T23:08:00	Donna Noble	PH2x6	50000	5000000						3	0.313
2015-03-28T13:19:00	Jason U	Server7	50000	5000000						3	0.313
2016-02-17T17:30:52	arnaud	SPR18	50000	5000000						3	0.313
2016-06-05T08:40:09	Jason U	Server7	50000	5000000						3	0.313
2017-02-20T16:58:07	Bruce	eleven	50000	5000000						3	0.313
2017-09-05T09:27:38	Sebastian Hornbostel	V2	50000	5000000						3	0.313
2018-02-20T14:22:45	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2018-12-30T02:57:41	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2020-09-08T23:37:45	mnd9	75203b	50000	5000000						7	0.730
2020-10-05T02:11:30	mnd9	75204	50000	5000000						7	0.730
2020-11-01T10:59:55	daveward2005	Dave2	50000	5000000						7	0.730
2020-12-06T16:19:57	lycorn	colab_A	50000	5000000						7	0.730
2021-01-08T10:37:46	Zenzoma	AMD3970X	50000	5000000						7	0.730
2021-02-09T00:10:34	mnd9	50869	50000	5000000						7	0.730
2021-03-08T15:30:18	Zenzoma	AMD3970X	50000	5000000						7	0.730
2021-06-06T22:25:51	kutens	vega	50000	5000000	665547649852780673970143	79.139	3	2	3050360735420129	3	0.313

date	userid	compid	res64	spent (GHz-days)
1998-07-29T00:00:00	ANONYMOUS	v4_computers	9973D37151A97C6E	0.218
1999-05-02T00:00:00	ANONYMOUS	v4_computers	9973D37151A97C6E	0.218
2018-09-06T01:43:38	kkmrkkblmbrbk	old	9973D37151A97C6E	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 = 2817421, B2 = 28174210 (P-1 stage 2)

B1 = 2817421 (P-1 stage 1)

B1 = 336067, B2 = 3360670 (P-1 stage 2)

B1 = 499280 (P-1 stage 1)

B1 = 336067 (P-1 stage 1)

B1 = 135059, B2 = 3630000 (P-1 stage 2)

B1 = 135059, B2 = 3300000 (P-1 stage 2)

B1 = 233380 (P-1 stage 1)

B1 = 194484 (P-1 stage 1)

B1 = 135059 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

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10¹⁰

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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