M2205187 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	13.4746	67.1642%	2000000	242000000	1.4373	9.2676%	14.9119	70.2073%	3.0431%
PrimeNet	2⁵⁸	0.0174	62.0690%	10000	180000	0.0018	2.8643%	0.0192	63.1554%	1.0865%
GPU72	2⁶²	0.2786	64.5161%	11000	170000	0.0019	1.6008%	0.2805	65.0841%	0.5680%
Difference	+5	+13.1960	+2.6481%	+1989000	+241830000	+1.4354	+7.6668%	+14.6314	+5.1231%	+5.1231%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.4746

67.1642%

2000000

242000000

1.4373

9.2676%

14.9119

70.2073%

3.0431%

PrimeNet

2⁵⁸

0.0174

62.0690%

10000

180000

0.0018

2.8643%

0.0192

63.1554%

1.0865%

GPU72

2⁶²

0.2786

64.5161%

11000

170000

0.0019

1.6008%

0.2805

65.0841%

0.5680%

Difference

+13.1960

+2.6481%

+1989000

+241830000

+1.4354

+7.6668%

+14.6314

+5.1231%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2205187	233749823	9	27.800	53 53	-	1	53	8.201e-12	3.654e-7	5.457e-7
2205187	99403179116009	14	46.498	22538492 2² × 5634623	2014-02-13	4	5634623	6.213e-6	0.0293	0.0547
2205187	7044907014841414350479	22	72.577	1597349117068397 7 × 11 × 20744793728161	2022-05-15	11	20744793728161	440.90	107,754	201,254

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2205187

233749823

27.800

53
53

8.201e-12

3.654e-7

5.457e-7

2205187

99403179116009

46.498

22538492
2² × 5634623

2014-02-13

5634623

6.213e-6

0.0293

0.0547

2205187

7044907014841414350479

72.577

1597349117068397
7 × 11 × 20744793728161

2022-05-15

20744793728161

440.90

107,754

201,254

exponent	prime factors	composite factor	digits	bits*
2205187	233749823 99403179116009	23235475524004400216407	23	74.299
2205187	233749823 7044907014841414350479	1646745767770638977494126215217	31	100.377
2205187	99403179116009 7044907014841414350479	700286153851909385178570410125718311	36	119.075
2205187	233749823 99403179116009 7044907014841414350479	163691764512234586997529656759924062944108953	45	146.876

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-04-11T11:38:05	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 233749823 skipped known factor: 99403179116009	-	-	0.123	-	-	5.184%
2021-06-28T04:40:29	Dylan Delgado	laptop-ryzen73700	1000000	106000000		-	skipped known factor: 233749823 skipped known factor: 99403179116009	-	-	0.641	-	-	7.726%
2021-07-02T10:50:23	Dylan Delgado	laptop-ryzen73700	2000000	242000000		-	skipped known factor: 233749823 skipped known factor: 99403179116009	-	-	1.437	-	-	9.268%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-02-13T14:46:00	TJAOI	Manual testing	?	?	99403179116009	46.498	14	1.96175e-6	0.312	4.22095e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.526 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	1.526 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.645	52.446%
25	50000	0.061	94.117%
30	250000	0.004	99.616%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.257
50000	6319859		7	0.665
50000	7150000	7044907014841414350479	6	0.605

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-17T23:54:48	Gordon Spence	haswell	50000	5000000						3	0.257
2022-05-15T23:10:34	debrouxl	dl380g9-1	50000	7150000	7044907014841414350479	72.577	6	2	2569933481172644	6	0.605
2022-07-06T08:54:15	debrouxl	dl380g9-1	50000	6319859						7	0.665

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T16:11:36

Oliver Kruse

GTX-2

233749823

99403179116009

F5CEA9EBF196F2__

2017-11-20T01:52:55

kkmrkkblmbrbk

c4.xlarge

233749823

99403179116009

F5CEA9EBF196F2__

2022-05-15T23:56:48

aperson1

2012_VP113

233749823

99403179116009

7044907014841414350479

32B2DEA287D312__

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 = 2000000, B2 = 242000000 (P-1 stage 2)

B1 = 1000000, B2 = 106000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

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

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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