M4923419 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	6.0352	65.6716%	-	-	-	-	6.0352	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0624	62.2951%	22000	450000	0.0091	3.3047%	0.0715	63.5411%	1.2461%
GPU72	2⁶⁵	1.4818	64.6154%	32000	700000	0.0137	2.3759%	1.4956	65.4561%	0.8407%
Difference	+2	+4.5534	+1.0563%	-32000	-700000	-0.0137	-2.3759%	+4.5396	+0.2156%	+0.2156%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.0352

65.6716%

6.0352

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0624

62.2951%

22000

450000

0.0091

3.3047%

0.0715

63.5411%

1.2461%

GPU72

2⁶⁵

1.4818

64.6154%

32000

700000

0.0137

2.3759%

1.4956

65.4561%

0.8407%

Difference

+4.5534

+1.0563%

-32000

-700000

-0.0137

-2.3759%

+4.5396

+0.2156%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4923419	9846839	7	23.231	1 1	-	1	1	2.270e-13	2.010e-7	4.090e-7
4923419	38638992313	11	35.169	3924 2² × 3² × 109	2008-09-08	9	109	1.719e-9	2.904e-6	3.681e-6
4923419	258114494909017	15	47.875	26212932 2² × 3² × 19² × 2017	2008-09-08	361	2017	6.835e-6	9.069e-5	0.0001
4923419	32677883114755222319111	23	74.791	3318616911820345 5 × 663723382364069	2019-08-09	5	663723382364069	1,447.4	7,267,955	13,574,517

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4923419

9846839

23.231

1
1

2.270e-13

2.010e-7

4.090e-7

4923419

38638992313

35.169

3924
2² × 3² × 109

2008-09-08

109

1.719e-9

2.904e-6

3.681e-6

4923419

258114494909017

47.875

26212932
2² × 3² × 19² × 2017

2008-09-08

361

2017

6.835e-6

9.069e-5

0.0001

4923419

32677883114755222319111

74.791

3318616911820345
5 × 663723382364069

2019-08-09

663723382364069

1,447.4

7,267,955

13,574,517

exponent	prime factors	composite factor	digits	bits*
4923419	9846839 38638992313	380471936428348607	18	58.401
4923419	9846839 258114494909017	2541611874935410047263	22	71.106
4923419	38638992313 258114494909017	9973283984663385497386321	25	83.044
4923419	9846839 32677883114755222319111	321773853891813198585492640129	30	98.022
4923419	9846839 38638992313 258114494909017	98205321698258826187698023689319	32	106.276
4923419	38638992313 32677883114755222319111	1262640474476139532064735961993743	34	109.960
4923419	258114494909017 32677883114755222319111	8434635294860939418080290221685323887	37	122.666
4923419	9846839 38638992313 32677883114755222319111	12433017467050155313776792595262506328377	41	133.191
4923419	9846839 258114494909017 32677883114755222319111	83054495772213197838590306886209692978143193	44	145.897
4923419	38638992313 258114494909017 32677883114755222319111	325905808321090326579163027092508295574708280631	48	157.835
4923419	9846839 38638992313 258114494909017 32677883114755222319111	32091420237026367502824390825325672926885649113402 75409	55	181.066

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T00:19:00	Will Edgington	Manual testing	?	?	258114494909017	47.875	15	3.02669e-6	1.449	6.42626e-6
2008-09-08T00:19:00	Will Edgington	Manual testing	?	?	38638992313	35.169	11	7.89648e-10	1.449	1.67659e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.420 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.420 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.065	93.752%
25	50000	0.006	99.419%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	32677883114755222319111	2	0.420

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-08-09T21:56:44	MarkS	laptop64	50000	5000000	32677883114755222319111	74.791	2	2		2	0.420

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-20T17:06:54

kkmrkkblmbrbk

c4.xlarge

9846839

38638992313

258114494909017

B7F60F26BB6A4B__

2018-04-11T11:27:19

Oliver Kruse

GTX-7

9846839

38638992313

258114494909017

B7F60F26BB6A4B__

2019-08-10T09:05:16

Niels_Mache_Nextcloud

SuperDry-X

9846839

38638992313

258114494909017

32677883114755222319111

B7F60F26BB6A4B74

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

10¹⁴

10¹⁵

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