M5041703 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

FE7B26323AA788A3

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	2⁷²	189.6846	68.0556%	300000	9375000	0.1597	2.9456%	189.8443	68.9965%	0.9410%
PrimeNet	2⁶¹	0.0609	62.2951%	22000	450000	0.0091	3.3178%	0.0700	63.5461%	1.2510%
GPU72	2⁶⁵	1.4471	64.6154%	34000	700000	0.0141	2.4194%	1.4612	65.4715%	0.8561%
Difference	+7	+188.2376	+3.4402%	+266000	+8675000	+0.1455	+0.5262%	+188.3831	+3.5250%	+3.5250%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

189.6846

68.0556%

300000

9375000

0.1597

2.9456%

189.8443

68.9965%

0.9410%

PrimeNet

2⁶¹

0.0609

62.2951%

22000

450000

0.0091

3.3178%

0.0700

63.5461%

1.2510%

GPU72

2⁶⁵

1.4471

64.6154%

34000

700000

0.0141

2.4194%

1.4612

65.4715%

0.8561%

Difference

+188.2376

+3.4402%

+266000

+8675000

+0.1455

+0.5262%

+188.3831

+3.5250%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5041703	39423302070469013114809	23	75.061	3909720789827268 2² × 3 × 13 × 79 × 7853 × 40397869	2021-10-24	7853	40397869	1,553.2	0.4439	0.8262

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5041703

39423302070469013114809

75.061

3909720789827268
2² × 3 × 13 × 79 × 7853 × 40397869

2021-10-24

7853

40397869

1,553.2

0.4439

0.8262

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	10000	10000		-		-	-	0.002	-	-	0.076%
2009-07-23T19:19:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	1.154%
2014-11-22T16:18:00	Jocelyn Larouche	Manual testing	67731	67731		-		-	-	0.014	-	-	0.406%
2017-03-04T04:53:01	Squeeky_Squirrel	i5-5250U_1600	300000	9375000	12	-		-	-	0.160	-	-	2.946%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-10-24T07:57:39	ATH	5960X	2500000	92500000	2	7	39423302070469013114809	P-1	23	75.061	1.730

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-10-24T07:57:39

ATH

5960X

2500000

92500000

39423302070469013114809

P-1

75.061

1.730

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2016-02-23T16:39:07	Mark Rose	Manual testing	2⁶¹	2⁶³		-	-	0.256	-	-
2014-12-16T14:36:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.389	-	-
2014-12-16T14:36:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.741	-	-
2015-07-30T21:27:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.482	-	-
2016-05-18T12:49:23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.964	-	-
2018-06-11T12:29:26	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.929	-	-
2020-12-28T10:15:13	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.86	-	-
2021-03-27T16:29:59	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.71	-	-
2021-03-27T16:30:00	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.43	-	-
2021-04-02T10:14:55	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.86	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-07-08T09:18:00	Martti Järvi	HAL	50000	5000000						3	0.632
2014-05-25T10:58:00	driveByUpgrades	Build_4	50000	5000000						3	0.632
2017-07-01T08:05:17	deo2016	deo2016.home.new	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	88D144EE396309__	0.699
2015-11-13T21:36:52	MadPoo	Manual testing	4E6B673CC1C682__	0.699

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 = 92500000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 300000, B2 = 9375000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 67731 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 10000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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