M4719839 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	6.2955	65.6716%	-	-	-	-	6.2955	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0651	62.2951%	20000	400000	0.0078	3.1242%	0.0729	63.4730%	1.1780%
GPU72	2⁶⁵	1.5458	64.6154%	30000	650000	0.0122	2.2801%	1.5579	65.4222%	0.8068%
Difference	+2	+4.7498	+1.0563%	-30000	-650000	-0.0122	-2.2801%	+4.7376	+0.2494%	+0.2494%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.2955

65.6716%

6.2955

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0651

62.2951%

20000

400000

0.0078

3.1242%

0.0729

63.4730%

1.1780%

GPU72

2⁶⁵

1.5458

64.6154%

30000

650000

0.0122

2.2801%

1.5579

65.4222%

0.8068%

Difference

+4.7498

+1.0563%

-30000

-650000

-0.0122

-2.2801%

+4.7376

+0.2494%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4719839	9439679	7	23.170	1 1	-	1	1	2.368e-13	1.909e-7	3.885e-7
4719839	10619637751	11	33.306	1125 3² × 5³	2008-09-08	125	125	3.015e-10	2.386e-5	4.857e-5
4719839	20234440656257	14	44.202	2143552 2⁶ × 33493	2008-09-30	64	33493	9.793e-7	0.0004	0.0007
4719839	9098598873063240744823	22	72.946	963867504067749 3² × 53 × 769 × 10369 × 253417	2019-04-22	10369	253417	363.56	0.0045	0.0049

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4719839

9439679

23.170

1
1

2.368e-13

1.909e-7

3.885e-7

4719839

10619637751

33.306

1125
3² × 5³

2008-09-08

125

3.015e-10

2.386e-5

4.857e-5

4719839

20234440656257

44.202

2143552
2⁶ × 33493

2008-09-30

33493

9.793e-7

0.0004

0.0007

4719839

9098598873063240744823

72.946

963867504067749
3² × 53 × 769 × 10369 × 253417

2019-04-22

10369

253417

363.56

0.0045

0.0049

exponent	prime factors	composite factor	digits	bits*
4719839	9439679 10619637751	100245971465721929	18	56.476
4719839	9439679 20234440656257	191006624539615421503	21	67.372
4719839	10619637751 20234440656257	214882429863556051558007	24	77.508
4719839	9439679 9098598873063240744823	85887852711478739330850031817	29	96.116
4719839	9439679 10619637751 20234440656257	2028421160651982925215035959753	31	100.678
4719839	10619637751 9098598873063240744823	96623824073588448424123688613073	32	106.252
4719839	20234440656257 9098598873063240744823	184105058952084961696539485595307511	36	117.148
4719839	9439679 10619637751 9098598873063240744823	912097883007147331231783476803364323567	39	129.422
4719839	9439679 20234440656257 9098598873063240744823	1737892658783758419142628154844826810128969	43	140.318
4719839	10619637751 20234440656257 9098598873063240744823	1955129034197641959391959727290048352269447761	46	150.454
4719839	9439679 10619637751 20234440656257 9098598873063240744823	18455790486405762653591135006545596339902508371108 719	53	173.624

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T21:36:00	markr	Manual testing	?	?	20234440656257	44.202	14	4.82785e-7	1.329	1.03214e-6
2008-09-08T00:11:00	Will Edgington	Manual testing	?	?	10619637751	33.306	11	5.90387e-11	1.329	1.26218e-10

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.592 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:	0.592 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	9098598873063240744823	3	0.592

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-04-22T16:41:57	ATH	ec2-ECMCF	50000	5000000	9098598873063240744823	72.946	3	2	3496521132735595	3	0.592

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-18T17:25:24

Ducho_YYZ

Pantalaimon

9439679

10619637751

20234440656257

BA8B91EE5C4F58__

2018-01-05T08:40:04

kkmrkkblmbrbk

c4.xlarge

9439679

10619637751

20234440656257

BA8B91EE5C4F58__

2019-04-22T17:45:04

ATH

ec2-PRPCF

9439679

10619637751

20234440656257

9098598873063240744823

BA8B91EE5C4F584A

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

10⁴

10⁵

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