M1030357 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	28.8385	70.1493%	10000000	1000000000	2.7478	11.6420%	31.5863	73.6245%	3.4752%
PrimeNet	2⁵⁶	0.0093	64.2857%	4500	60000	0.0003	1.9511%	0.0096	64.9825%	0.6968%
GPU72	2⁶⁰	0.1491	66.6667%	4500	18000	0.0002	0.6148%	0.1493	66.8716%	0.2049%
Difference	+7	+28.6894	+3.4826%	+9995500	+999982000	+2.7476	+11.0272%	+31.4370	+6.7529%	+6.7529%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

28.8385

70.1493%

10000000

1000000000

2.7478

11.6420%

31.5863

73.6245%

3.4752%

PrimeNet

2⁵⁶

0.0093

64.2857%

4500

60000

0.0003

1.9511%

0.0096

64.9825%

0.6968%

GPU72

2⁶⁰

0.1491

66.6667%

4500

18000

0.0002

0.6148%

0.1493

66.8716%

0.2049%

Difference

+28.6894

+3.4826%

+9995500

+999982000

+2.7476

+11.0272%

+31.4370

+6.7529%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1030357	41214281	8	25.297	20 2² × 5	-	4	5	4.357e-12	1.742e-7	3.499e-7
1030357	1687724767	10	30.652	819 3² × 7 × 13	2008-07-16	9	13	1.634e-10	3.962e-7	7.872e-7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1030357

41214281

25.297

20
2² × 5

4.357e-12

1.742e-7

3.499e-7

1030357

1687724767

30.652

819
3² × 7 × 13

2008-07-16

1.634e-10

3.962e-7

7.872e-7

exponent	prime factors	composite factor	digits	bits*
1030357	41214281 1687724767	69558362797797527	17	55.949

exponent

prime factors

composite factor

digits

bits*

1030357

41214281
1687724767

69558362797797527

55.949

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T18:59:21	alpertron	Manual testing	300000	10000000	12	-	skipped known factor: 41214281 skipped known factor: 1687724767	-	-	0.036	-	-	4.080%
2021-07-21T10:31:17	ViliamF	3	10000000	1000000000		-	skipped known factor: 41214281 skipped known factor: 1687724767	-	-	2.748	-	-	11.642%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-07-04T16:57:22	Dylan Delgado	desktoplinux	3000000	243000000	2	7			-	-	0.645

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-07-04T16:57:22

Dylan Delgado

desktoplinux

3000000

243000000

0.645

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-16T09:30:00	J Feitsma	Manual testing	?	?	1687724767	30.652	10	2.46103e-11	0.071	5.73958e-11

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.483 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.483 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	9.81
250000	25000000		44	7.677

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-09T18:20:47	TJAOI	Manual testing	50000	5000000						100	3.490
2017-04-21T14:30:10	TJAOI	Manual testing	50000	5000000						90	3.141
2017-09-22T15:56:14	TJAOI	Manual testing	50000	5000000						91	3.176
2020-02-17T11:28:13	TJAOI	Manual testing	250000	25000000						44	7.677

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T18:29:08

Oliver Kruse

GTX-0

41214281

1687724767

37175CF205E2AC__

2017-10-18T10:03:43

kkmrkkblmbrbk

c4.xlarge

41214281

1687724767

37175CF205E2AC__

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 = 10000000, B2 = 1000000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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