M5049689 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

62AA7940B27AD55C

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	189.3847	68.0556%	300000	9450000	0.1605	2.9511%	189.5452	68.9983%	0.9427%
PrimeNet	2⁶¹	0.0608	62.2951%	22000	500000	0.0097	3.4039%	0.0705	63.5785%	1.2834%
GPU72	2⁶⁵	1.4448	64.6154%	34000	700000	0.0141	2.4200%	1.4589	65.4717%	0.8563%
Difference	+7	+187.9399	+3.4402%	+266000	+8750000	+0.1464	+0.5311%	+188.0862	+3.5266%	+3.5266%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

189.3847

68.0556%

300000

9450000

0.1605

2.9511%

189.5452

68.9983%

0.9427%

PrimeNet

2⁶¹

0.0608

62.2951%

22000

500000

0.0097

3.4039%

0.0705

63.5785%

1.2834%

GPU72

2⁶⁵

1.4448

64.6154%

34000

700000

0.0141

2.4200%

1.4589

65.4717%

0.8563%

Difference

+187.9399

+3.4402%

+266000

+8750000

+0.1464

+0.5311%

+188.0862

+3.5266%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5049689	33711381424688814011017	23	74.836	3337966102931172 2² × 3³ × 599 × 2753 × 18742397	2021-10-30	2753	18742397	1,468.1	0.2058	0.3833

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5049689

33711381424688814011017

74.836

3337966102931172
2² × 3³ × 599 × 2753 × 18742397

2021-10-30

2753

18742397

1,468.1

0.2058

0.3833

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-06-11T00:00:00	ANONYMOUS	v4_computers	25000	306250		-		-	-	0.008	-	-	0.648%
2009-08-09T21:24:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	1.154%
2017-03-07T04:17:28	Squeeky_Squirrel	i5-5250U_1600	300000	9450000	12	-		-	-	0.160	-	-	2.951%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-10-30T20:19:28	ATH	5960X	2500000	87500000	2	7	33711381424688814011017	P-1	23	74.836	1.676

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-10-30T20:19:28

ATH

5960X

2500000

87500000

33711381424688814011017

P-1

74.836

1.676

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2016-02-23T16:39:07	Mark Rose	Manual testing	2⁶¹	2⁶³		-	-	0.255	-	-
2014-12-17T21:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.389	-	-
2014-12-17T21:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.740	-	-
2015-07-30T21:28:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.480	-	-
2016-05-19T12:46:47	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.960	-	-
2018-06-11T12:29:27	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.919	-	-
2020-12-21T16:08:26	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.84	-	-
2021-04-01T12:54:16	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.68	-	-
2021-04-01T12:54:16	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.35	-	-
2021-04-03T17:56:53	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.71	-	-

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
2010-07-13T09:28:00	alan145	Bear4	50000	5000000						3	0.632
2014-05-30T07:36:00	Brett Walker		50000	5000000						3	0.632
2017-07-06T10:42:54	bayanne	iMac	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	27A373C04BB273__	0.700
2000-08-10T00:00:00	ANONYMOUS	v4_computers	2AB7C784CB9144__	0.700

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 = 87500000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 300000, B2 = 9450000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

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

B1 = 55000 (P-1 stage 1)

B1 = 25000, B2 = 306250 (P-1 stage 2)

B1 = 25000 (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