M1817177 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	16.3517	68.6567%	500000	15000000	0.1015	5.0643%	16.4532	70.2440%	1.5873%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8753%	0.0118	64.2172%	1.0593%
GPU72	2⁶¹	0.1690	65.5738%	9000	130000	0.0012	1.5574%	0.1703	66.1099%	0.5361%
Difference	+6	+16.1826	+3.0829%	+491000	+14870000	+0.1002	+3.5069%	+16.2829	+4.1341%	+4.1341%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3517

68.6567%

500000

15000000

0.1015

5.0643%

16.4532

70.2440%

1.5873%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8753%

0.0118

64.2172%

1.0593%

GPU72

2⁶¹

0.1690

65.5738%

9000

130000

0.0012

1.5574%

0.1703

66.1099%

0.5361%

Difference

+16.1826

+3.0829%

+491000

+14870000

+0.1002

+3.5069%

+16.2829

+4.1341%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1817177	25440479	8	24.601	7 7	-	1	7	1.232e-12	1.044e-7	1.601e-7
1817177	69052727	8	26.041	19 19	2008-07-15	1	19	4.940e-12	1.558e-7	1.601e-7
1817177	159101517252823612954689887	27	87.040	43777110664735359559 111577 × 392348877140767	2020-06-13	111577	392348877140767	26,279,163	1,681,509	3,140,591

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1817177

25440479

24.601

7
7

1.232e-12

1.044e-7

1.601e-7

1817177

69052727

26.041

19
19

2008-07-15

4.940e-12

1.558e-7

1.601e-7

1817177

159101517252823612954689887

87.040

43777110664735359559
111577 × 392348877140767

2020-06-13

111577

392348877140767

26,279,163

1,681,509

3,140,591

exponent	prime factors	composite factor	digits	bits*
1817177	25440479 69052727	1756734451136233	16	50.642
1817177	25440479 159101517252823612954689887	4047618808538596816077916021735873	34	111.641
1817177	69052727 159101517252823612954689887	10986393636145018924513864136671849	35	113.081
1817177	25440479 69052727 159101517252823612954689887	279499116586080994903697545777853304375671	42	137.682

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:37:38	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 25440479 skipped known factor: 69052727	-	-	0.101	-	-	5.064%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	69052727	26.041	8	2.02329e-14	0.211	4.33200e-14

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:46:00

J Feitsma

Manual testing

69052727

26.041

2.02329e-14

0.211

4.33200e-14

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.088 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:	18.088 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.304	0.025%
25	50000	0.751	47.177%
30	250000	0.046	95.470%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		10	0.690
50000	5000000	159101517252823612954689887	148	10.21
50000	6500000		93	7.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-18T13:29:37	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-02T13:56:25	alpertron		50000	5000000						3	0.207
2018-09-28T16:57:38	alpertron	Manual testing	50000	5000000						3	0.207
2020-05-02T02:34:52	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-13T08:03:51	nordi	sweet16	50000	5000000	159101517252823612954689887	87.040	148	2	7113959082800950	148	10.21
2021-03-12T16:34:57	TJAOI	Manual testing	50000	6500000						93	7.184

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T22:25:41

Oliver Kruse

GTX-2

25440479

69052727

7B7E956B9CCB0E__

2017-11-05T22:03:58

kkmrkkblmbrbk

c4.xlarge

25440479

69052727

7B7E956B9CCB0E__

2020-06-13T18:37:17

CrypticClue

cruncher

25440479

69052727

159101517252823612954689887

41C709BA2F21ABAC

2020-06-15T00:43:11

Team_Inspector

SpudBoy4

25440479

69052727

159101517252823612954689887

41C709BA2F21ABAC

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

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