M3616621 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

1527596F2E1FA0__

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	33.0106	68.1159%	30000000	1000000000	12.6170	11.8527%	45.6276	71.8951%	3.7791%
PrimeNet	2⁶⁰	0.0425	63.3333%	15000	300000	0.0046	2.9775%	0.0471	64.4251%	1.0918%
GPU72	2⁶⁴	0.9842	65.6250%	20000	400000	0.0062	1.9821%	0.9904	66.3063%	0.6813%
Difference	+5	+32.0264	+2.4909%	+29980000	+999600000	+12.6108	+9.8706%	+44.6372	+5.5887%	+5.5887%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

33.0106

68.1159%

30000000

1000000000

12.6170

11.8527%

45.6276

71.8951%

3.7791%

PrimeNet

2⁶⁰

0.0425

63.3333%

15000

300000

0.0046

2.9775%

0.0471

64.4251%

1.0918%

GPU72

2⁶⁴

0.9842

65.6250%

20000

400000

0.0062

1.9821%

0.9904

66.3063%

0.6813%

Difference

+32.0264

+2.4909%

+29980000

+999600000

+12.6108

+9.8706%

+44.6372

+5.5887%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3616621	56383765967057675544103	23	75.578	7795089113160831 3 × 17 × 5399 × 28309850819	2021-08-12	5399	28309850819	2,936.0	234.89	438.71

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3616621

56383765967057675544103

75.578

7795089113160831
3 × 17 × 5399 × 28309850819

2021-08-12

5399

28309850819

2,936.0

234.89

438.71

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:50:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.824%
2011-12-16T18:58:00	markr	tiny	240000	6180000		-		-	-	0.086	-	-	3.426%
2020-06-11T11:19:57	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	11.085%
2020-08-06T10:54:52	axn	Manual testing	30000000	1000000000	12	-		-	-	12.62	-	-	11.853%
2022-03-04T04:19:28	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.717%
2022-03-22T11:10:06	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.764%
2022-05-25T14:13:18	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.851%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-07-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-12T16:38:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-29T07:34:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.085	-	-
2012-06-05T02:29:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.441	-	-
2016-02-23T16:29:35	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.271	-	-
2015-01-20T20:49:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.543	-	-
2015-01-20T20:49:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.033	-	-
2015-10-18T15:17:02	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.066	-	-
2016-12-23T23:58:57	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.132	-	-
2018-11-26T14:19:27	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.265	-	-
2020-10-20T12:03:51	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.53	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.130 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	4.130 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.878	41.541%
25	50000	0.079	92.419%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.225
50000	5000000	56383765967057675544103	5	0.742
50000	6300000		7	1.162

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-09T18:06:00	Dougal	dougal	50000	5000000						3	0.445
2012-05-03T03:30:00	Smurgs	Praca	50000	5000000						3	0.445
2015-08-17T11:32:00	driveByUpgrades	Build_4	50000	5000000						3	0.445
2017-04-21T08:18:55	Bruce	desk	50000	5000000						3	0.445
2020-11-09T18:15:24	axn	Manual testing	50000	5000000						3	0.445
2021-06-25T03:12:38	kutens	capella	50000	6300000						7	1.162
2021-08-12T06:41:30	MarkS	desktop-i7	50000	5000000	56383765967057675544103	75.578	5	2	8244342715138397	5	0.742

date	userid	compid	res64	spent (GHz-days)
1999-08-07T00:00:00	Jonathan Champ	v4_computers	938A6287F1FE23__	0.380
2000-02-01T00:00:00	jbafford	v4_computers	4E6C36BE13E436__	0.380

date

userid

compid

res64

spent (GHz-days)

1999-08-07T00:00:00

Jonathan Champ

v4_computers

938A6287F1FE23__

0.380

2000-02-01T00:00:00

jbafford

v4_computers

4E6C36BE13E436__

0.380

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 = 30000000, B2 = 1000000000 (P-1 stage 2)

B1 = 30000000, B2 = 600000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

B1 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 240000, B2 = 6180000 (P-1 stage 2)

B1 = 240000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 245000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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