M4844951 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	Prob over default TF
Actual	2⁶⁷	6.1330	65.6716%	-	-	-	-	6.1330	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0634	62.2951%	20000	450000	0.0087	3.2297%	0.0721	63.5129%	1.2178%
GPU72	2⁶⁵	1.5058	64.6154%	32000	650000	0.0132	2.3258%	1.5190	65.4384%	0.8230%
Difference	+2	+4.6271	+1.0563%	-32000	-650000	-0.0132	-2.3258%	+4.6139	+0.2333%	+0.2333%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.1330

65.6716%

6.1330

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0634

62.2951%

20000

450000

0.0087

3.2297%

0.0721

63.5129%

1.2178%

GPU72

2⁶⁵

1.5058

64.6154%

32000

650000

0.0132

2.3258%

1.5190

65.4384%

0.8230%

Difference

+4.6271

+1.0563%

-32000

-650000

-0.0132

-2.3258%

+4.6139

+0.2333%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4844951	37218913583	11	35.115	3841 23 × 167	-	23	167	1.730e-9	6.200e-6	9.408e-6
4844951	201984689363329	15	47.521	20844864 2⁶ × 3⁴ × 4021	2014-03-07	81	4021	7.257e-6	5.942e-5	8.223e-5
4844951	64763185069304735513	20	65.812	6683574825556 2² × 1670893706389	2019-05-21	4	1670893706389	2.5127	18,297	34,173
4844951	1068151164564880296961	22	69.856	110233433172480 2⁹ × 3 × 5 × 41 × 73 × 4795627	2019-06-25	512	4795627	30.410	0.0526	0.0981

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4844951

37218913583

35.115

3841
23 × 167

167

1.730e-9

6.200e-6

9.408e-6

4844951

201984689363329

47.521

20844864
2⁶ × 3⁴ × 4021

2014-03-07

4021

7.257e-6

5.942e-5

8.223e-5

4844951

64763185069304735513

65.812

6683574825556
2² × 1670893706389

2019-05-21

1670893706389

2.5127

18,297

34,173

4844951

1068151164564880296961

69.856

110233433172480
2⁹ × 3 × 5 × 41 × 73 × 4795627

2019-06-25

512

4795627

30.410

0.0526

0.0981

exponent	prime factors	composite factor	digits	bits*
4844951	37218913583 201984689363329	7517650698502841340197807	25	82.637
4844951	37218913583 64763185069304735513	2410415388454288816951018173079	31	100.927
4844951	37218913583 1068151164564880296961	39755425887521091569330836521263	32	104.971
4844951	201984689363329 64763185069304735513	13081171818403303716865980706202777	35	113.333
4844951	201984689363329 1068151164564880296961	215750181167715461574088623543543169	36	117.377
4844951	64763185069304735513 1068151164564880296961	69176871552708721123012147494387002675993	41	135.667
4844951	37218913583 201984689363329 64763185069304735513	486867003473527530079737635496706469237619991	45	148.448
4844951	37218913583 201984689363329 1068151164564880296961	8029987348397795793858961631650552444640964527	46	152.492
4844951	37218913583 64763185069304735513 1068151164564880296961	25746880042625569210478358302528398301561732157129 19	52	170.783
4844951	201984689363329 64763185069304735513 1068151164564880296961	13972668911700781707993446291778768518140749166442 860697	56	183.189
4844951	37218913583 201984689363329 64763185069304735513 1068151164564880296961	52004755674846205194335521786406578883084151105671 6115788950147351	66	218.304

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-03-07T11:24:00	TJAOI	Manual testing	?	?	201984689363329	47.521	15	3.38730e-6	1.428	7.20376e-6
2019-05-21T13:16:07	TJAOI	Manual testing	2⁶⁵	2⁶⁶*	64763185069304735513	65.812	20	1.007	1.365	2.046

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.209 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.209 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1068151164564880296961	1	0.209

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-06-26T02:54:52	ATH	ec2-ECMCF	50000	5000000	1068151164564880296961	69.856	1	2	2851413812293510	1	0.209

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:30:05

kkmrkkblmbrbk

Manual testing

37218913583

201984689363329

535A8D61811612__

2018-03-29T22:54:37

Oliver Kruse

GTX-2

37218913583

201984689363329

535A8D61811612__

2019-05-23T04:42:15

fre_games

gpu

37218913583

201984689363329

64763185069304735513

DC00689FBFE93822

2019-05-27T04:50:50

Chang Chia-Tche

exbpc13

37218913583

201984689363329

64763185069304735513

DC00689FBFE93822

2019-06-26T17:40:16

Niels_Mache_Nextcloud

SuperDry-X

37218913583

201984689363329

64763185069304735513

1068151164564880296961

DC00689FBFE93822

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

10⁰

10¹

10²

10³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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