M1417901 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	20.9563	68.6567%	1500000	181500000	0.6260	8.3059%	21.5822	71.2601%	2.6034%
PrimeNet	2⁵⁶	0.0068	62.5000%	6500	110000	0.0007	2.7690%	0.0074	63.5384%	1.0384%
GPU72	2⁶⁰	0.1083	65.0000%	6000	80000	0.0006	1.3012%	0.1089	65.4554%	0.4554%
Difference	+7	+20.8479	+3.6567%	+1494000	+181420000	+0.6254	+7.0047%	+21.4734	+5.8046%	+5.8046%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.9563

68.6567%

1500000

181500000

0.6260

8.3059%

21.5822

71.2601%

2.6034%

PrimeNet

2⁵⁶

0.0068

62.5000%

6500

110000

0.0007

2.7690%

0.0074

63.5384%

1.0384%

GPU72

2⁶⁰

0.1083

65.0000%

6000

80000

0.0006

1.3012%

0.1089

65.4554%

0.4554%

Difference

+20.8479

+3.6567%

+1494000

+181420000

+0.6254

+7.0047%

+21.4734

+5.8046%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1417901	144625903	9	27.108	51 3 × 17	-	3	17	1.275e-11	2.083e-7	3.380e-7
1417901	175021959398690801081	21	67.246	61718681134540 2² × 5 × 19 × 162417581933	2018-09-17	19	162417581933	33.459	489.89	914.99
1417901	61558160654960298967129	23	75.704	21707496029327964 2² × 3 × 38601677 × 46862161	2019-01-25	38601677	46862161	6,756.4	2.1620	4.3493

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1417901

144625903

27.108

51
3 × 17

1.275e-11

2.083e-7

3.380e-7

1417901

175021959398690801081

67.246

61718681134540
2² × 5 × 19 × 162417581933

2018-09-17

162417581933

33.459

489.89

914.99

1417901

61558160654960298967129

75.704

21707496029327964
2² × 3 × 38601677 × 46862161

2019-01-25

38601677

46862161

6,756.4

2.1620

4.3493

exponent	prime factors	composite factor	digits	bits*
1417901	144625903 175021959398690801081	25312708922864994124133001143	29	94.354
1417901	144625903 61558160654960298967129	8902904571742704667270998942487	31	102.812
1417901	175021959398690801081 61558160654960298967129	10774029894810546977051611417166917896666449	44	142.950
1417901	144625903 175021959398690801081 61558160654960298967129	15582038024859703704800095788128752025322458764284 47	52	170.058

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:14:03	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 144625903	-	-	0.071	-	-	4.915%
2021-07-01T14:16:45	Dylan Delgado	desktoplinux	1500000	181500000		-	skipped known factor: 144625903	-	-	0.626	-	-	8.306%

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.425 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.425 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		191	9.006
50000	5000000	175021959398690801081	1	0.047
50000	5000000	61558160654960298967129	59	2.782
250000	35000000		50	13.59

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-17T06:31:22	storm5510	HP-Z220-CMT	50000	5000000						3	0.141
2018-09-17T18:27:00	Chang Chia-Tche	exbpc13	50000	5000000	175021959398690801081	67.246	1	2		1	0.047
2018-11-23T15:01:57	Chang Chia-Tche	exbpc13	50000	5000000						3	0.141
2019-01-25T12:26:34	TJAOI	Manual testing	50000	5000000	61558160654960298967129	75.704	59	2		59	2.782
2019-01-25T12:26:34	TJAOI	Manual testing	50000	5000000						185	8.723
2021-11-19T10:15:39	TJAOI	Manual testing	250000	35000000						50	13.59

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T19:26:14

Oliver Kruse

GTX-2

144625903

7F45A092CFB5A0__

2017-10-26T11:06:00

kkmrkkblmbrbk

c4.xlarge

144625903

7F45A092CFB5A0__

2018-09-20T17:07:13

Justine V.

Gible_Desktop_1

144625903

175021959398690801081

7363DDAFD98336__

2018-09-24T17:26:12

Oliver Kruse

GTX-4

144625903

175021959398690801081

7363DDAFD98336__

2019-01-25T13:18:38

ATH

work102442

144625903

175021959398690801081

61558160654960298967129

7363DDAFD9833650

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 = 1500000, B2 = 181500000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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