M1004987 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	29.5665	70.1493%	10000000	1110000000	3.0054	11.7636%	32.5719	73.6608%	3.5115%
PrimeNet	2⁵⁶	0.0096	64.2857%	4500	60000	0.0003	1.9407%	0.0099	64.9788%	0.6931%
GPU72	2⁶⁰	0.1528	66.6667%	4500	16000	0.0002	0.5777%	0.1530	66.8592%	0.1926%
Difference	+7	+29.4136	+3.4826%	+9995500	+1109984000	+3.0052	+11.1858%	+32.4188	+6.8015%	+6.8015%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

29.5665

70.1493%

10000000

1110000000

3.0054

11.7636%

32.5719

73.6608%

3.5115%

PrimeNet

2⁵⁶

0.0096

64.2857%

4500

60000

0.0003

1.9407%

0.0099

64.9788%

0.6931%

GPU72

2⁶⁰

0.1528

66.6667%

4500

16000

0.0002

0.5777%

0.1530

66.8592%

0.1926%

Difference

+29.4136

+3.4826%

+9995500

+1109984000

+3.0052

+11.1858%

+32.4188

+6.8015%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1004987	8039897	7	22.939	4 2²	-	4	4	5.565e-13	1.719e-7	3.499e-7
1004987	573753447127736089	18	58.993	285453168612 2² × 3 × 23787764051	2012-04-06	4	23787764051	0.0433	55.698	104.03
1004987	137112377356271468910651138343	30	96.791	68215995508534672045833 3² × 47 × 2919361 × 55240557389711	2018-02-09	2919361	55240557389711	2.624e+10	129,344	241,579

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1004987

8039897

22.939

4
2²

5.565e-13

1.719e-7

3.499e-7

1004987

573753447127736089

58.993

285453168612
2² × 3 × 23787764051

2012-04-06

23787764051

0.0433

55.698

104.03

1004987

137112377356271468910651138343

96.791

68215995508534672045833
3² × 47 × 2919361 × 55240557389711

2018-02-09

2919361

55240557389711

2.624e+10

129,344

241,579

exponent	prime factors	composite factor	digits	bits*
1004987	8039897 573753447127736089	4612918618301943998742833	25	81.932
1004987	8039897 137112377356271468910651138343	1102369391369554914080337355210470671	37	119.730
1004987	573753447127736089 137112377356271468910651138343	78668699152039701192221702699701785176332760527	47	155.784
1004987	8039897 573753447127736089 137112377356271468910651138343	63248823830638653749623969087022428353384223236274 5719	54	178.723

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T18:58:57	alpertron	Manual testing	300000	10000000	12	-	skipped known factor: 8039897	-	-	0.036	-	-	4.067%
2021-06-18T10:08:11	ViliamF	3	10000000	1110000000		-	skipped known factor: 8039897	-	-	3.005	-	-	11.764%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.427 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:	17.427 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		573753447127736089	1	0.00000e+0
50000	5000000		276	9.60
50000	5000000	137112377356271468910651138343	5	0.174
250000	25000000		44	7.653

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-04-06T21:58:00	James Heinrich	Manual testing			573753447127736089	58.993		1		1	-
2017-02-03T18:31:48	TJAOI	Manual testing	50000	5000000						100	3.479
2017-03-03T18:15:30	TJAOI	Manual testing	50000	5000000						90	3.131
2018-02-09T12:21:59	TJAOI	Manual testing	50000	5000000	137112377356271468910651138343	96.791	5	2		5	0.174
2018-02-09T12:21:59	TJAOI	Manual testing	50000	5000000						86	2.992
2020-04-06T09:18:17	TJAOI	Manual testing	250000	25000000						44	7.653

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T16:14:43

Oliver Kruse

GTX-1

8039897

573753447127736089

633977F780A0D0__

2017-10-15T14:41:00

Oliver Kruse

Threadripper

8039897

573753447127736089

633977F780A0D0__

2017-12-25T12:28:59

ATH

ec2-1xf

8039897

573753447127736089

633977F780A0D0__

2018-02-12T05:19:32

AdolfNor

Manual testing

8039897

573753447127736089

137112377356271468910651138343

D8C815AB66851E__

2018-02-12T21:28:32

Oliver Kruse

GTX-3

8039897

573753447127736089

137112377356271468910651138343

D8C815AB66851E__

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 = 1110000000 (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

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