M1638799 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	18.1315	68.6567%	500000	15000000	0.0835	5.0016%	18.2151	70.2244%	1.5677%
PrimeNet	2⁵⁷	0.0117	63.1579%	7000	120000	0.0009	2.5600%	0.0126	64.1011%	0.9432%
GPU72	2⁶¹	0.1874	65.5738%	6500	70000	0.0006	1.1196%	0.1881	65.9592%	0.3854%
Difference	+6	+17.9441	+3.0829%	+493500	+14930000	+0.0829	+3.8819%	+18.0270	+4.2652%	+4.2652%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.1315

68.6567%

500000

15000000

0.0835

5.0016%

18.2151

70.2244%

1.5677%

PrimeNet

2⁵⁷

0.0117

63.1579%

7000

120000

0.0009

2.5600%

0.0126

64.1011%

0.9432%

GPU72

2⁶¹

0.1874

65.5738%

6500

70000

0.0006

1.1196%

0.1881

65.9592%

0.3854%

Difference

+17.9441

+3.0829%

+493500

+14930000

+0.0829

+3.8819%

+18.0270

+4.2652%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1638799	410332185477287	15	48.544	125192957 19 × 6589103	-	19	6589103	2.386e-5	0.0233	0.0434
1638799	56829794009105608223	20	65.623	17338854249089 17338854249089	2017-12-11	1	17338854249089	5.4280	61,183	114,273
1638799	278938587756115950791	21	67.919	85104575898605 5 × 31 × 1489 × 368745319	2019-11-04	1489	368745319	20.994	1.3013	2.4302

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1638799

410332185477287

48.544

125192957
19 × 6589103

6589103

2.386e-5

0.0233

0.0434

1638799

56829794009105608223

65.623

17338854249089
17338854249089

2017-12-11

17338854249089

5.4280

61,183

114,273

1638799

278938587756115950791

67.919

85104575898605
5 × 31 × 1489 × 368745319

2019-11-04

1489

368745319

20.994

1.3013

2.4302

exponent	prime factors	composite factor	digits	bits*
1638799	410332185477287 56829794009105608223	23319093575980336011121545686931001	35	114.167
1638799	410332185477287 278938587756115950791	114457480327915066935776822140184017	36	116.462
1638799	56829794009105608223 278938587756115950791	15852022483370897221950763574063992954393	41	133.542
1638799	410332185477287 56829794009105608223 278938587756115950791	65045950298366706775141322021373016527749660439283 71791	55	182.086

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:17:44	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 410332185477287	-	-	0.084	-	-	5.002%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.106 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.106 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	9.654	0.006%
25	50000	0.893	40.933%
30	250000	0.056	94.522%
35	1000000	0.003	99.737%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		242	13.60
50000	5000000	56829794009105608223	2	0.112
50000	5000000	278938587756115950791	7	0.393

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-11T13:16:38	ATH	ec2-1xe	50000	5000000	56829794009105608223	65.623	2	2		2	0.112
2018-05-23T07:32:20	Chang Chia-Tche	exbpc13	50000	5000000						3	0.169
2019-11-04T17:15:14	TJAOI	Manual testing	50000	5000000	278938587756115950791	67.919	7	2		7	0.393
2019-11-04T17:15:15	TJAOI	Manual testing	50000	5000000						239	13.43

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T16:34:40

Oliver Kruse

GTX-0

410332185477287

689D4A0C9A42BB__

2017-11-02T01:04:02

ATH

ec2-1xf

410332185477287

689D4A0C9A42BB__

2017-12-12T13:26:56

Oliver Kruse

Threadripper

410332185477287

56829794009105608223

3B928F35849D6D__

2017-12-12T18:40:16

kkmrkkblmbrbk

c4.xlarge

410332185477287

56829794009105608223

3B928F35849D6D__

2019-11-05T10:15:53

mnd9

75202b

410332185477287

56829794009105608223

278938587756115950791

3B928F35849D6D3D

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

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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