M2106617 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	56.6723	68.1159%	2500000	125000000	0.8746	7.2759%	57.5469	70.4358%	2.3198%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6793%	0.0199	63.0853%	1.0163%
GPU72	2⁶²	0.2916	64.5161%	10000	140000	0.0016	1.4522%	0.2933	65.0314%	0.5153%
Difference	+7	+56.3806	+3.5998%	+2490000	+124860000	+0.8730	+5.8237%	+57.2537	+5.4044%	+5.4044%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2106617	132967885262884169903716583	27	86.781	31559577574586213323 12109 × 27791 × 93781835417	2021-12-26	27791	93781835417	14,657,731	487.13	909.82

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	-	-	0.180%
2009-08-02T00:52:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.753%
2010-12-29T20:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.297%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.437%
2011-01-24T23:16:00	James Heinrich	Q6600	140000	3010000		-		-	-	0.028	-	-	2.466%
2016-07-17T03:53:37	Jocelyn Larouche	Manual testing	186340	6020000	12	-		-	-	0.048	-	-	3.031%
2016-11-08T17:01:21	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.089%
2017-05-31T03:38:55	Jocelyn Larouche	low 4M	372680	3726800	6	-		-	-	0.053	-	-	3.025%
2017-06-10T03:57:32	Jocelyn Larouche	low 4M	447216	4472160	6	-		-	-	0.064	-	-	3.231%
2017-07-10T02:37:02	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.276%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	S00030	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-02T19:33:00	Sturle Sunde	fungo.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-29T23:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2013-09-04T10:21:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.466	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.932	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.774	-	-
2015-12-27T16:49:17	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.547	-	-
2016-10-01T21:16:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.095	-	-
2019-05-20T13:24:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.19	-	-
2021-09-02T11:43:56	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	28.38	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.938 GHz-days
Estimated T-Level:	23.464

Digits	B1	Curves	Complete	FacMiss
20	11000	194 / 100	1.940	14.231%
25	50000	194 / 280	0.693	49.953%

New Calculation Method

Total ECM effort:	16.938 GHz-days
Estimated T-Level:	23.464

Digits	B1	Complete	FacMiss
20	11000	7.557	0.052%
25	50000	0.700	49.639%
30	250000	0.044	95.664%
35	1000000	0.002	99.792%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		160	13.62
50000	5000000	132967885262884169903716583	5	0.426
50000	5150000		7	0.603
50000	6750000		21	2.043
76620	24176890		1	0.245

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-17T06:49:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.255
2009-11-12T06:24:00	KAMCOBILL	PC01	50000	5000000						3	0.255
2011-06-22T21:16:00	S36049	Wolle5	50000	5000000						3	0.255
2013-04-07T09:24:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-10-26T22:08:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.255
2015-08-02T14:04:00	guru	w6	50000	5000000						3	0.255
2016-04-24T23:31:10	lettp	Home	50000	5000000						3	0.255
2016-05-28T09:38:32	Bruce	Desk6	50000	5000000						3	0.255
2016-08-17T03:59:47	Bruce	test	50000	5000000						3	0.255
2017-02-11T11:46:09	Bruce	Desk6	50000	5000000						3	0.255
2017-08-29T03:54:28	Bruce	Desk6	50000	5000000						3	0.255
2017-12-08T17:22:06	Sid & Andy	Barrel_Of_Monkeys	50000	5000000						67	5.704
2020-07-11T20:57:09	GAN	LMS-16	50000	5000000						3	0.255
2020-07-17T19:32:31	daveward2005	Dave2	50000	5000000						3	0.255
2020-07-23T19:30:16	gLauss	laptop-klaus	50000	5000000						3	0.255
2020-07-30T21:36:53	GAN	LMS-13	50000	5000000						3	0.255
2020-08-07T09:51:11	mat10243x	K2	50000	5000000						3	0.255
2020-08-16T00:04:39	GAN	LMS-08	50000	5000000						3	0.255
2020-09-12T10:41:20	GAN	XPS	50000	5000000						7	0.596
2020-10-13T04:35:54	daveward2005	Dave2	50000	5000000						7	0.596
2020-11-09T21:38:04	Bruno Victal	Manual testing	76620	24176890						1	0.245
2020-11-10T15:32:42	lycorn	colab_D_1	50000	5000000						7	0.596
2020-12-23T18:01:11	C.D.B.	i7-6850K	50000	5000000						7	0.596
2021-01-24T00:01:25	lycorn	colab_DG	50000	6750000						7	0.681
2021-02-23T04:13:05	Zenzoma	AMD3970X	50000	5000000						7	0.596
2021-05-13T19:42:33	kutens	arcturus	50000	5150000						7	0.603
2021-05-28T12:14:20	GAN	KL-SCH09	50000	5000000						7	0.596
2021-06-25T08:03:36	kutens	terra	50000	6750000						7	0.681
2021-08-13T03:18:49	kutens	ryzen3	50000	6750000						7	0.681
2021-12-26T20:55:31	Kamil Mudrunka	LinuxServer	50000	5000000	132967885262884169903716583	86.781	5	2	3568324867541840	5	0.426

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	S00030	v4_computers	537E9D9E030EFD47	0.139
2018-04-02T11:56:18	kkmrkkblmbrbk	old	537E9D9E030EFD47	0.139

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 = 447216, B2 = 4472160 (P-1 stage 2)

B1 = 372680, B2 = 3726800 (P-1 stage 2)

B1 = 186340, B2 = 6020000 (P-1 stage 2)

B1 = 447216 (P-1 stage 1)

B1 = 372680 (P-1 stage 1)

B1 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 223608 (P-1 stage 1)

B1 = 186340 (P-1 stage 1)

B1 = 140000 (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)

10²

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10⁹

10¹⁰

10¹¹

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