M2006231 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	14.8108	68.6567%	500000	15000000	0.1230	5.1250%	14.9338	70.2631%	1.6063%
PrimeNet	2⁵⁸	0.0191	63.7931%	8000	140000	0.0014	2.4803%	0.0206	64.6912%	0.8981%
GPU72	2⁶²	0.3062	66.1290%	8000	110000	0.0013	1.2375%	0.3075	66.5482%	0.4191%
Difference	+5	+14.5046	+2.5277%	+492000	+14890000	+0.1217	+3.8875%	+14.6263	+3.7149%	+3.7149%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.8108

68.6567%

500000

15000000

0.1230

5.1250%

14.9338

70.2631%

1.6063%

PrimeNet

2⁵⁸

0.0191

63.7931%

8000

140000

0.0014

2.4803%

0.0206

64.6912%

0.8981%

GPU72

2⁶²

0.3062

66.1290%

8000

110000

0.0013

1.2375%

0.3075

66.5482%

0.4191%

Difference

+14.5046

+2.5277%

+492000

+14890000

+0.1217

+3.8875%

+14.6263

+3.7149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2006231	16049849	8	23.936	4 2²	-	4	4	5.575e-13	3.813e-7	7.761e-7
2006231	179674688803087379397449	24	77.250	44779162719319804 2² × 907 × 12342657860893	2021-07-25	907	12342657860893	18,836	64,111	119,741

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2006231

16049849

23.936

4
2²

5.575e-13

3.813e-7

7.761e-7

2006231

179674688803087379397449

77.250

44779162719319804
2² × 907 × 12342657860893

2021-07-25

907

12342657860893

18,836

64,111

119,741

exponent	prime factors	composite factor	digits	bits*
2006231	16049849 179674688803087379397449	2883751624411543173134767435201	31	101.186

exponent

prime factors

composite factor

digits

bits*

2006231

16049849
179674688803087379397449

2883751624411543173134767435201

101.186

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:19:27	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 16049849	-	-	0.123	-	-	5.125%

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.215 GHz-days
Estimated T-Level:	1.850

Digits	B1	Curves	Complete	FacMiss
20	11000	37 / 100	0.370	68.945%
25	50000	37 / 280	0.132	87.601%

New Calculation Method

Total ECM effort:	3.215 GHz-days
Estimated T-Level:	1.850

Digits	B1	Complete	FacMiss
20	11000	1.209	29.846%
25	50000	0.110	89.618%
30	250000	0.007	99.326%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.285
50000	5000000	179674688803087379397449	3	0.254
50000	6750000		7	0.676

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-25T05:53:20	Gordon Spence	haswell	50000	5000000						3	0.254
2019-05-12T00:54:12	ATH	ec2-ECMCF	50000	5000000						3	0.254
2021-04-14T23:13:14	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.592
2021-07-25T18:34:10	MarkS	desktop-i7	50000	5000000	179674688803087379397449	77.250	3	2	2311211170829115	3	0.254
2021-08-28T21:51:52	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.592
2021-12-04T09:07:57	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.592
2022-04-25T15:48:44	Dylan Delgado	colab	50000	6750000						7	0.676

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T20:16:15

Oliver Kruse

GTX-2

16049849

BDA2346C980804__

2017-11-13T11:15:14

kkmrkkblmbrbk

c4.xlarge

16049849

BDA2346C980804__

2021-07-25T19:18:33

SRJ2877

LTOS

16049849

179674688803087379397449

DAF1264AA42AF7CA

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

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