M1947779 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	15.2553	68.6567%	500000	15000000	0.1015	5.1068%	15.3568	70.2574%	1.6006%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4662%	0.0209	64.6860%	0.8929%
GPU72	2⁶²	0.3154	66.1290%	8000	90000	0.0010	1.1528%	0.3164	66.5195%	0.3905%
Difference	+5	+14.9399	+2.5277%	+492000	+14910000	+0.1005	+3.9540%	+15.0404	+3.7378%	+3.7378%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2553

68.6567%

500000

15000000

0.1015

5.1068%

15.3568

70.2574%

1.6006%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4662%

0.0209

64.6860%

0.8929%

GPU72

2⁶²

0.3154

66.1290%

8000

90000

0.0010

1.1528%

0.3164

66.5195%

0.3905%

Difference

+14.9399

+2.5277%

+492000

+14910000

+0.1005

+3.9540%

+15.0404

+3.7378%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1947779	15582233	8	23.893	4 2²	-	4	4	5.742e-13	3.146e-7	6.404e-7
1947779	26411883241	11	34.620	6780 2² × 3 × 5 × 113	2008-07-15	5	113	1.724e-9	8.562e-7	9.306e-7
1947779	9686223165106340833919	22	73.036	2486479001238421 7³ × 150617 × 48130091	2021-04-05	150617	48130091	1,938.9	0.2175	0.3853

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1947779

15582233

23.893

4
2²

5.742e-13

3.146e-7

6.404e-7

1947779

26411883241

34.620

6780
2² × 3 × 5 × 113

2008-07-15

113

1.724e-9

8.562e-7

9.306e-7

1947779

9686223165106340833919

73.036

2486479001238421
7³ × 150617 × 48130091

2021-04-05

150617

48130091

1,938.9

0.2175

0.3853

exponent	prime factors	composite factor	digits	bits*
1947779	15582233 26411883241	411556118630057153	18	58.514
1947779	15582233 9686223165106340833919	150932986248684472651540161127	30	96.930
1947779	26411883241 9686223165106340833919	255831395283058139454219200451479	33	107.657
1947779	15582233 26411883241 9686223165106340833919	3986424410015712881522136414508650972607	40	131.550

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:19:11	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 15582233 skipped known factor: 26411883241	-	-	0.101	-	-	5.107%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	26411883241	34.620	11	5.49358e-10	0.234	1.21747e-9

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:48:00

J Feitsma

Manual testing

26411883241

34.620

5.49358e-10

0.234

1.21747e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.999 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	20.999 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.076	0.011%
25	50000	0.806	44.642%
30	250000	0.050	95.123%
35	1000000	0.002	99.770%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		35	2.435
50000	5000000	9686223165106340833919	5	0.348
50000	7500000		218	18.22

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-06-25T08:05:04	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-12T11:25:47	alpertron		50000	5000000						3	0.209
2018-09-28T16:58:24	alpertron	Manual testing	50000	5000000						3	0.209
2021-01-11T15:51:47	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.487
2021-04-05T09:32:51	MarkS	desktop-i7	50000	5000000	9686223165106340833919	73.036	5	2	5950546183628360	5	0.348
2021-06-15T15:29:45	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.487
2021-09-13T18:12:51	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.487
2022-01-03T07:46:55	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.487
2022-04-28T10:17:53	TJAOI	Manual testing	50000	7500000						218	18.22

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T04:48:51

Oliver Kruse

GTX-2

15582233

26411883241

8EB44A2367805C__

2017-11-11T10:24:17

kkmrkkblmbrbk

c4.xlarge

15582233

26411883241

8EB44A2367805C__

2021-04-07T08:17:59

Joe S.

VMWare2

15582233

26411883241

9686223165106340833919

C168FDC4A7B9CD5D

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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