M3709943 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

A6757746FC84B766

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	2⁷⁰	64.4082	68.5714%	14000000	700000000	7.8239	10.2446%	72.2321	71.7912%	3.2197%
PrimeNet	2⁶⁰	0.0414	63.3333%	16000	320000	0.0050	3.0851%	0.0464	64.4645%	1.1312%
GPU72	2⁶⁴	0.9594	65.6250%	22000	450000	0.0069	2.1066%	0.9663	66.3492%	0.7242%
Difference	+6	+63.4488	+2.9464%	+13978000	+699550000	+7.8170	+8.1380%	+71.2658	+5.4420%	+5.4420%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

64.4082

68.5714%

14000000

700000000

7.8239

10.2446%

72.2321

71.7912%

3.2197%

PrimeNet

2⁶⁰

0.0414

63.3333%

16000

320000

0.0050

3.0851%

0.0464

64.4645%

1.1312%

GPU72

2⁶⁴

0.9594

65.6250%

22000

450000

0.0069

2.1066%

0.9663

66.3492%

0.7242%

Difference

+63.4488

+2.9464%

+13978000

+699550000

+7.8170

+8.1380%

+71.2658

+5.4420%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3709943	163259022609883279434983	24	77.112	22002901744027237 11 × 18457 × 108374264231	2021-09-26	18457	108374264231	12,709	899.21	1,679.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3709943

163259022609883279434983

77.112

22002901744027237
11 × 18457 × 108374264231

2021-09-26

18457

108374264231

12,709

899.21

1,679.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-08-24T00:00:00	estrand	v4_computers	15000	142500		-		-	-	0.003	-	-	0.531%
2010-09-12T13:35:00	markr	tiny	100000	2150000		-		-	-	0.032	-	-	2.058%
2015-10-19T21:22:15	mikr	MSI	1600000	66000000	12	-		-	-	0.778	-	-	6.142%
2021-05-05T04:04:53	axn	Manual testing	14000000	700000000		-		-	-	7.824	-	-	10.245%
2022-03-04T04:18:13	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.622%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-07T07:42:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-15T08:10:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.083	-	-
2012-04-19T23:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.430	-	-
2016-02-23T16:29:37	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.265	-	-
2015-01-20T20:48:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.529	-	-
2015-01-20T20:48:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.007	-	-
2016-02-23T09:49:01	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.014	-	-
2016-10-30T14:39:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.028	-	-
2022-01-18T20:12:53	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.057	-	-
2019-01-07T14:44:09	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.057	-	-
2020-12-17T10:34:01	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.11	-	-
2021-03-05T16:26:31	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.23	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.983 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	2.983 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.645	52.458%
25	50000	0.058	94.336%
30	250000	0.004	99.642%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	2.833
50000	5000000	163259022609883279434983	1	0.149

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-26T23:50:00	Ryan Schulz	T7400	50000	5000000						3	0.447
2012-05-16T14:54:00	oodaira	Linux01	50000	5000000						3	0.447
2015-11-08T17:08:07	Bruce	agent86	50000	5000000						3	0.447
2017-06-12T10:28:46	Claude Portenier	Petit-Idiot	50000	5000000						3	0.447
2021-07-28T21:22:46	RIHATEC	i7-3770K	50000	5000000						7	1.044
2021-09-26T04:34:20	daveward2005	Dave2	50000	5000000	163259022609883279434983	77.112	1	2	3488973286881245	1	0.149

date	userid	compid	res64	spent (GHz-days)
2000-08-31T00:00:00	estrand	v4_computers	C4498EFCD76605__	0.390

date

userid

compid

res64

spent (GHz-days)

2000-08-31T00:00:00

estrand

v4_computers

C4498EFCD76605__

0.390

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 = 14000000, B2 = 700000000 (P-1 stage 2)

B1 = 14000000 (P-1 stage 1)

B1 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 100000, B2 = 2150000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 15000, B2 = 142500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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