M4965419 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	5.9842	65.6716%	-	-	-	-	5.9842	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0619	62.2951%	22000	450000	0.0091	3.3094%	0.0710	63.5429%	1.2478%
GPU72	2⁶⁵	1.4693	64.6154%	34000	700000	0.0141	2.4132%	1.4834	65.4693%	0.8539%
Difference	+2	+4.5149	+1.0563%	-34000	-700000	-0.0141	-2.4132%	+4.5007	+0.2024%	+0.2024%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.9842

65.6716%

5.9842

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0619

62.2951%

22000

450000

0.0091

3.3094%

0.0710

63.5429%

1.2478%

GPU72

2⁶⁵

1.4693

64.6154%

34000

700000

0.0141

2.4132%

1.4834

65.4693%

0.8539%

Difference

+4.5149

+1.0563%

-34000

-700000

-0.0141

-2.4132%

+4.5007

+0.2024%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4965419	39723353	8	25.243	4 2²	-	4	4	9.010e-13	8.039e-7	1.636e-6
4965419	210096808729	12	37.612	21156 2² × 3 × 41 × 43	2008-09-08	41	43	5.823e-9	8.262e-6	1.677e-5
4965419	101351972135154975823	21	66.458	10205782446069 3⁴ × 7 × 151 × 661 × 180337	2019-08-20	661	180337	4.4655	0.0021	0.0037

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4965419

39723353

25.243

4
2²

9.010e-13

8.039e-7

1.636e-6

4965419

210096808729

37.612

21156
2² × 3 × 41 × 43

2008-09-08

5.823e-9

8.262e-6

1.677e-5

4965419

101351972135154975823

66.458

10205782446069
3⁴ × 7 × 151 × 661 × 180337

2019-08-20

661

180337

4.4655

0.0021

0.0037

exponent	prime factors	composite factor	digits	bits*
4965419	39723353 210096808729	8345749697315548337	19	62.856
4965419	39723353 101351972135154975823	4026040166370924814323494519	28	91.701
4965419	210096808729 101351972135154975823	21293725903986592692257450358967	32	104.070
4965419	39723353 210096808729 101351972135154975823	845858190769303528781763067489222856351	39	129.314

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T00:21:00	Will Edgington	Manual testing	?	?	210096808729	37.612	12	2.13581e-9	1.462	4.53725e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.631 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.631 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	101351972135154975823	3	0.631

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-08-20T06:40:20	MarkS	laptop64	50000	5000000	101351972135154975823	66.458	3	2		3	0.631

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:35:45

kkmrkkblmbrbk

Manual testing

39723353

210096808729

844EDB32A9B891__

2018-04-22T09:17:26

Oliver Kruse

GTX-1

39723353

210096808729

844EDB32A9B891__

2019-08-20T18:38:02

mnd9

75204b

39723353

210096808729

101351972135154975823

638393CAD420F8CA

2019-08-20T19:49:28

ATH

ec2-PRPCFDC

39723353

210096808729

101351972135154975823

638393CAD420F8CA

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

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