M2372417 Mersenne number exponent details

Residue

Status

L-L

3242D340671515F8

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	25.1241	67.6471%	3000000	100000000	0.8115	7.8378%	25.9357	70.1828%	2.5358%
PrimeNet	2⁵⁹	0.0324	62.7119%	10000	170000	0.0018	2.4742%	0.0342	63.6345%	0.9226%
GPU72	2⁶³	0.6727	65.0794%	10000	140000	0.0017	1.2718%	0.6744	65.5235%	0.4441%
Difference	+5	+24.4514	+2.5677%	+2990000	+99860000	+0.8099	+6.5660%	+25.2612	+4.6593%	+4.6593%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

25.1241

67.6471%

3000000

100000000

0.8115

7.8378%

25.9357

70.1828%

2.5358%

PrimeNet

2⁵⁹

0.0324

62.7119%

10000

170000

0.0018

2.4742%

0.0342

63.6345%

0.9226%

GPU72

2⁶³

0.6727

65.0794%

10000

140000

0.0017

1.2718%

0.6744

65.5235%

0.4441%

Difference

+24.4514

+2.5677%

+2990000

+99860000

+0.8099

+6.5660%

+25.2612

+4.6593%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2372417	1947650918516954648521	22	70.722	410478199767780 2² × 3 × 5 × 6841303329463	2020-04-04	5	6841303329463	184.50	36,511	68,193

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2372417

1947650918516954648521

70.722

410478199767780
2² × 3 × 5 × 6841303329463

2020-04-04

6841303329463

184.50

36,511

68,193

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.231%
2010-10-10T16:19:00	Oscar Östlin		40000	630000		-		-	-	0.007	-	-	1.440%
2011-01-18T00:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.523%
2011-01-27T03:45:00	James Heinrich	i7-920	160000	3640000		-		-	-	0.034	-	-	3.008%
2016-01-12T09:09:51	mikr	MSI	3000000	100000000	12	-		-	-	0.812	-	-	7.838%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:13	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-16T05:44:00	Sturle Sunde	jodel.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-31T12:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.129	-	-
2013-01-23T08:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.414	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.828	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.575	-	-
2015-10-30T09:42:39	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.150	-	-
2017-06-16T21:40:02	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.300	-	-
2019-04-08T13:40:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.60	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.644 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	3.644 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.323	26.645%
25	50000	0.120	88.733%
30	250000	0.007	99.267%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.466
50000	5000000	1947650918516954648521	2	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-28T01:05:00	SubPrime	pitr	50000	5000000						3	0.267
2010-02-11T03:26:00	James Classen	towerofart	50000	5000000						3	0.267
2012-01-15T20:28:00	S36049	Wolle5	50000	5000000						3	0.267
2013-11-09T19:35:00	Bruce	apandya-DESK11	50000	5000000						3	0.267
2015-06-21T08:13:00	Jayder	HPJared	50000	5000000						3	0.267
2016-02-18T23:23:36	Sintax	cloud	50000	5000000						3	0.267
2016-05-17T00:49:46	Bruce	Desk6	50000	5000000						3	0.267
2016-09-07T23:10:15	Bruce	Desk6	50000	5000000						3	0.267
2017-03-13T10:09:42	Bruce	Desk6	50000	5000000						3	0.267
2017-10-21T13:49:00	Bruce	Desk6	50000	5000000						3	0.267
2018-03-12T13:29:40	Bruce	Desk6	50000	5000000						3	0.267
2018-09-22T13:07:20	Bruce	Desk6	50000	5000000						3	0.267
2020-03-22T12:35:01	Keysarecool	HPLaptop	50000	5000000						3	0.267
2020-04-04T12:34:08	daveward2005	MW	50000	5000000	1947650918516954648521	70.722	2	2		2	0.178

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	3242D340671515F8	0.160
2018-05-13T21:58:33	kkmrkkblmbrbk	old	3242D340671515F8	0.160

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

ANONYMOUS

v4_computers

3242D340671515F8

0.160

2018-05-13T21:58:33

kkmrkkblmbrbk

old

3242D340671515F8

0.160

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 160000, B2 = 3640000 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 40000, B2 = 630000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 40000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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