M538771 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	55.1513	70.1493%	20000000	2460000000	3.2340	12.7572%	58.3853	73.9574%	3.8081%
PrimeNet	2⁴⁰	0.0000	50.0000%	5000	180000	0.0003	19.4313%	0.0003	59.7156%	9.7156%
GPU72	2⁴⁴	0.0000	54.5455%	9000	300000	0.0005	14.6544%	0.0005	61.2066%	6.6611%
Difference	+23	+55.1513	+15.6038%	+19991000	+2459700000	+3.2335	-1.8972%	+58.3848	+12.7508%	+12.7508%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

55.1513

70.1493%

20000000

2460000000

3.2340

12.7572%

58.3853

73.9574%

3.8081%

PrimeNet

2⁴⁰

0.0000

50.0000%

5000

180000

0.0003

19.4313%

0.0003

59.7156%

9.7156%

GPU72

2⁴⁴

0.0000

54.5455%

9000

300000

0.0005

14.6544%

0.0005

61.2066%

6.6611%

Difference

+23

+55.1513

+15.6038%

+19991000

+2459700000

+3.2335

-1.8972%

+58.3848

+12.7508%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
538771	9697879	7	23.209	9 3²	-	9	9	2.078e-12	1.903e-7	3.873e-7
538771	49023221547473	14	45.479	45495416 2³ × 967 × 5881	2014-01-22	967	5881	1.299e-5	2.611e-5	4.162e-5
538771	5884331357586306235679	22	72.317	5460883527125909 19 × 287414922480311	2015-06-19	19	287414922480311	3,238.7	331,126	618,451

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

538771

9697879

23.209

9
3²

2.078e-12

1.903e-7

3.873e-7

538771

49023221547473

45.479

45495416
2³ × 967 × 5881

2014-01-22

967

5881

1.299e-5

2.611e-5

4.162e-5

538771

5884331357586306235679

72.317

5460883527125909
19 × 287414922480311

2015-06-19

287414922480311

3,238.7

331,126

618,451

exponent	prime factors	composite factor	digits	bits*
538771	9697879 49023221547473	475421270757585909767	21	68.688
538771	9697879 5884331357586306235679	57065533501777729930560424841	29	95.527
538771	49023221547473 5884331357586306235679	288468879801696058497217535824889167	36	117.796
538771	9697879 49023221547473 5884331357586306235679	2797536291582392370082937499107940329976793	43	141.005

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:41:41	alpertron	Manual testing	1500000	50000000	12	-	skipped known factor: 9697879 skipped known factor: 49023221547473	-	-	0.088	-	-	6.149%
2021-08-07T19:32:46	ViliamF	3	20000000	2460000000		-	skipped known factor: 9697879 skipped known factor: 49023221547473	-	-	3.234	-	-	12.757%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-01-22T11:26:00	TJAOI	Manual testing	?	?	49023221547473	45.479	14	4.28588e-6	0.016	8.93219e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-01-22T11:26:00

TJAOI

Manual testing

49023221547473

45.479

4.28588e-6

0.016

8.93219e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.149 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	425 / 100	4.250	1.396%
25	50000	425 / 280	1.518	21.859%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	16.149 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	21.065	0.000%
25	50000	2.554	7.776%
30	250000	0.238	78.844%
35	1000000	0.018	98.227%
40	3000000	0.001	99.887%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		239	3.856
50000	5000000	5884331357586306235679	42	0.678
250000	25000000		144	11.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-05-06T03:01:00	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-06-19T10:51:00	TJAOI	Manual testing	50000	5000000						57	0.920
2015-06-19T10:51:00	TJAOI	Manual testing	50000	5000000	5884331357586306235679	72.317	42	2		42	0.678
2016-03-24T20:25:11	TJAOI	Manual testing	50000	5000000						90	1.452
2016-12-09T18:16:07	TJAOI	Manual testing	50000	5000000						91	1.468
2019-02-01T12:14:58	TJAOI	Manual testing	250000	25000000						44	3.549
2020-09-25T08:53:22	TJAOI	Manual testing	250000	25000000						100	8.066

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T10:27:25

Oliver Kruse

GTX-0

9697879

49023221547473

5884331357586306235679

045633B0E44F7A6F

2017-09-28T09:43:08

Oliver Kruse

Manual testing

9697879

49023221547473

5884331357586306235679

045633B0E44F7A__

2017-10-13T09:08:17

Oliver Kruse

GTX-3

045633B0E44F7A__

2017-12-17T07:44:54

ATH

xps

9697879

49023221547473

5884331357586306235679

045633B0E44F7A__

2020-04-19T04:36:18

Oliver Kruse

AddPrpType5

9697879

49023221547473

5884331357586306235679

C1083BE828E130__

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 = 20000000, B2 = 2460000000 (P-1 stage 2)

B1 = 20000000 (P-1 stage 1)

B1 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (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

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