M2106277 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	14.1073	67.1642%	500000	15000000	0.1230	5.1550%	14.2303	68.8569%	1.6927%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6793%	0.0199	63.0852%	1.0163%
GPU72	2⁶²	0.2917	64.5161%	10000	140000	0.0016	1.4522%	0.2933	65.0314%	0.5153%
Difference	+5	+13.8156	+2.6481%	+490000	+14860000	+0.1214	+3.7028%	+13.9370	+3.8255%	+3.8255%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.1073

67.1642%

500000

15000000

0.1230

5.1550%

14.2303

68.8569%

1.6927%

PrimeNet

2⁵⁸

0.0182

62.0690%

9000

160000

0.0016

2.6793%

0.0199

63.0852%

1.0163%

GPU72

2⁶²

0.2917

64.5161%

10000

140000

0.0016

1.4522%

0.2933

65.0314%

0.5153%

Difference

+13.8156

+2.6481%

+490000

+14860000

+0.1214

+3.7028%

+13.9370

+3.8255%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2106277	164289607	9	27.292	39 3 × 13	-	3	13	8.561e-12	3.380e-7	5.821e-7
2106277	7629105338321256198001	22	72.692	1811040366087000 2³ × 3² × 5³ × 829 × 242734267	2022-06-13	829	242734267	731.23	1.2609	2.3549

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2106277

164289607

27.292

39
3 × 13

8.561e-12

3.380e-7

5.821e-7

2106277

7629105338321256198001

72.692

1811040366087000
2³ × 3² × 5³ × 829 × 242734267

2022-06-13

829

242734267

731.23

1.2609

2.3549

exponent	prime factors	composite factor	digits	bits*
2106277	164289607 7629105338321256198001	1253382717794401220515898475607	31	99.984

exponent

prime factors

composite factor

digits

bits*

2106277

164289607
7629105338321256198001

1253382717794401220515898475607

99.984

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:13:25	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 164289607	-	-	0.123	-	-	5.155%

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.920 GHz-days
Estimated T-Level:	1.600

Digits	B1	Curves	Complete	FacMiss
20	11000	32 / 100	0.320	72.498%
25	50000	32 / 280	0.114	89.182%

New Calculation Method

Total ECM effort:	2.920 GHz-days
Estimated T-Level:	1.600

Digits	B1	Complete	FacMiss
20	11000	1.283	27.711%
25	50000	0.119	88.817%
30	250000	0.008	99.251%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	1.107
50000	5900000	7629105338321256198001	5	0.457
50000	6644605		7	0.676
50000	6750000		7	0.681

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-05T20:15:59	ATH	ec2-1xd	50000	5000000						3	0.255
2019-09-05T16:56:26	ATH	ec2-ECMCF	50000	5000000						3	0.255
2021-10-23T14:14:53	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.596
2022-03-11T20:25:11	Dylan Delgado	colab	50000	6750000						7	0.681
2022-06-13T15:42:39	debrouxl	z400	50000	5900000	7629105338321256198001	72.692	5	2	7540710672107323	5	0.457
2022-07-25T22:13:53	debrouxl	dl380g9-1	50000	6644605						7	0.676

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T03:14:09

Oliver Kruse

GTX-2

164289607

502D091DF343AF__

2017-11-17T04:40:30

ATH

ec2-1xf

164289607

502D091DF343AF__

2022-06-21T01:31:47

some-students

GIMPS_IN_SHANGHAI

164289607

7629105338321256198001

F2FF70DD1AFD1578

2022-06-21T04:04:25

Pierre

brollach

164289607

7629105338321256198001

F2FF70DD1AFD1578

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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