M515 861 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	2000000	6733146420	7.7971	46.1347%	7.7971	46.1347%
Target	2⁴⁴	0.0000	56.8182%	9000	300000	0.0005	14.5763%	0.0005	63.1125%
Difference	-44	0.0000	-56.8182%	+1991000	+6732846420	+7.7966	+31.5585%	+7.7966	-16.9778%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

2000000

6733146420

7.7971

46.1347%

7.7971

46.1347%

Target

2⁴⁴

0.0000

56.8182%

9000

300000

0.0005

14.5763%

0.0005

63.1125%

Difference

-44

0.0000

-56.8182%

+1991000

+6732846420

+7.7966

+31.5585%

+7.7966

-16.9778%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
515861	514829279	9	28.940	499 499	-	1	499	7.681e-11	5.949e-7	1.075e-6
515861	6680184571652141315153	22	72.500	6474791243815816 2³ × 37 × 1231 × 17769532691	2015-06-12	1231	17769532691	3,521.8	20.472	38.236
515861	18158493195028757447274293478967	32	103.840	17600180276303846818497903 3 × 37 × 83 × 4339 × 20693 × 367771 × 57852943	2022-12-18	367771	57852943	3.588e+11	0.0740	0.1245

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

515861

514829279

28.940

499
499

499

7.681e-11

5.949e-7

1.075e-6

515861

6680184571652141315153

72.500

6474791243815816
2³ × 37 × 1231 × 17769532691

2015-06-12

1231

17769532691

3,521.8

20.472

38.236

515861

18158493195028757447274293478967

103.840

17600180276303846818497903
3 × 37 × 83 × 4339 × 20693 × 367771 × 57852943

2022-12-18

367771

57852943

3.588e+11

0.0740

0.1245

exponent	prime factors	composite factor	digits	bits*
515861	514829279 6680184571652141315153	3439154606610595752086330764687	31	101.440
515861	514829279 18158493195028757447274293478967	9348523959323061580846105027010982274793	40	132.780
515861	6680184571652141315153 18158493195028757447274293478967	12130208608588150303398593610644216722265943112388 6951	54	176.341
515861	514829279 6680184571652141315153 18158493195028757447274293478967	62449865520790306286423291981819688206439187388060 878660838329	62	205.280

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16	alpertron	Manual testing	1500000	50000000	12	-	skipped known factor: 514829279	-	-	0.088	-	-	32.820%
2022-12-18	USAFSS	USAFSACS	2000000	6733146420			18158493195028757447274293478967	32	103.840	7.797	0.015	15.59	46.135%

ECM factoring results:

Total ECM effort:	16.101 GHz-days
Estimated T-Level:	26.435

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		195	3.137
50000	5000000	6680184571652141315153	86	1.383
250000	25000000		144	11.58

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-04-10	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-06-12	TJAOI	Manual testing	50000	5000000						13	0.209
2015-06-12	TJAOI	Manual testing	50000	5000000	6680184571652141315153	72.500	86	2		86	1.383
2016-03-18	TJAOI	Manual testing	50000	5000000						90	1.448
2016-08-12	TJAOI	Manual testing	50000	5000000						91	1.464
2018-05-04	TJAOI	Manual testing	250000	25000000						44	3.539
2020-10-16	TJAOI	Manual testing	250000	25000000						100	8.042

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-1

514829279

6680184571652141315153

85E0AC36931BC5__

2017-09-28

Oliver Kruse

Manual testing

514829279

6680184571652141315153

85E0AC36931BC5__

2017-11-07

kkmrkkblmbrbk

c4.xlarge

514829279

6680184571652141315153

85E0AC36931BC5__

2020-04-19

Oliver Kruse

AddPrpType5

514829279

6680184571652141315153

93727494886514__

2022-12-18

Kevin_9611

PRP-CF

514829279

6680184571652141315153

18158493195028757447274293478967

9372749488651463

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 = 2000000, B2 = 6733146420 (P-1 stage 2)

B1 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

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