M2087011 Mersenne number exponent details

Residue

Status

L-L

1AE3C7B4DD182370

double-checked

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	14.2375	68.6567%	500000	15000000	0.1230	5.1493%	14.3605	70.2707%	1.6140%
PrimeNet	2⁵⁸	0.0184	63.7931%	9000	160000	0.0016	2.6746%	0.0200	64.7615%	0.9684%
GPU72	2⁶²	0.2944	66.1290%	9000	140000	0.0015	1.3999%	0.2959	66.6032%	0.4741%
Difference	+5	+13.9432	+2.5277%	+491000	+14860000	+0.1214	+3.7495%	+14.0646	+3.6675%	+3.6675%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.2375

68.6567%

500000

15000000

0.1230

5.1493%

14.3605

70.2707%

1.6140%

PrimeNet

2⁵⁸

0.0184

63.7931%

9000

160000

0.0016

2.6746%

0.0200

64.7615%

0.9684%

GPU72

2⁶²

0.2944

66.1290%

9000

140000

0.0015

1.3999%

0.2959

66.6032%

0.4741%

Difference

+13.9432

+2.5277%

+491000

+14860000

+0.1214

+3.7495%

+14.0646

+3.6675%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2087011	47388048595491519599	20	65.361	11353090279709 181 × 197 × 227 × 349 × 4019	2002-03-10	349	4019	5.0063	5.234e-5	6.772e-5
2087011	749074833182561203305046729	27	89.275	179461160765937794124 2² × 3² × 1289 × 1915933 × 2018527807	2022-05-23	1915933	2018527807	104,073,491	10.657	19.583

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2087011

47388048595491519599

65.361

11353090279709
181 × 197 × 227 × 349 × 4019

2002-03-10

349

4019

5.0063

5.234e-5

6.772e-5

2087011

749074833182561203305046729

89.275

179461160765937794124
2² × 3² × 1289 × 1915933 × 2018527807

2022-05-23

1915933

2018527807

104,073,491

10.657

19.583

exponent	prime factors	composite factor	digits	bits*
2087011	47388048595491519599 749074833182561203305046729	35497194596514913770408113379039249797914341671	47	154.636

exponent

prime factors

composite factor

digits

bits*

2087011

47388048595491519599
749074833182561203305046729

35497194596514913770408113379039249797914341671

154.636

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T13:43:23	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 47388048595491519599	-	-	0.123	-	-	5.149%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-03-10T00:00:00	ANONYMOUS	v4_computers	?	?	47388048595491519599	65.361	20	1.511	0.279	3.067
1999-01-17T00:00:00	S00030	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.039 GHz-days
Estimated T-Level:	1.650

Digits	B1	Curves	Complete	FacMiss
20	11000	33 / 100	0.330	71.773%
25	50000	33 / 280	0.118	88.864%

New Calculation Method

Total ECM effort:	3.039 GHz-days
Estimated T-Level:	1.650

Digits	B1	Complete	FacMiss
20	11000	1.323	26.625%
25	50000	0.123	88.422%
30	250000	0.008	99.223%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	1.105
50000	6350000	749074833182561203305046729	6	0.566
50000	6750000		7	0.680
50000	6900000		7	0.687

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-05T17:19:32	Adam Buran		50000	5000000						3	0.255
2019-08-19T10:37:00	Malott	pm11	50000	5000000						3	0.255
2021-09-21T04:36:05	Dylan Delgado	colab	50000	6750000						7	0.680
2022-01-28T05:02:10	MarkS	desktop-i7	50000	5000000						7	0.595
2022-05-23T18:25:04	debrouxl	o9020	50000	6350000	749074833182561203305046729	89.275	6	2	127358798234009	6	0.566
2022-07-11T19:45:20	MarkS	desktop-i7	50000	6900000						7	0.687

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	S00030	v4_computers	1AE3C7B4DD182370	0.137

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

S00030

v4_computers

1AE3C7B4DD182370

0.137

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T18:21:23

Oliver Kruse

GTX-0

47388048595491519599

33E8A67CE88D83__

2017-11-16T22:14:25

kkmrkkblmbrbk

old

47388048595491519599

33E8A67CE88D83__

2022-05-30T01:45:46

kutens

terra

47388048595491519599

749074833182561203305046729

DEA9F03840EC398C

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

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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