M12 037 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
Actual	2⁶⁷	2,468.5484	79.1045%	100000000000	122192573512709700	1,903,855.2193	40.5533%	1,906,323.7677	87.5783%
Target	2⁴⁴	0.0002	68.1818%	500	80000	0.0000	1.3376%	0.0002	68.6074%
Difference	+23	+2,468.5482	+10.9227%	+99999999500	+122192573512629700	+1,903,855.2193	+39.2156%	+1,906,323.7675	+18.9709%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

2,468.5484

79.1045%

100000000000

122192573512709700

1,903,855.2193

40.5533%

1,906,323.7677

87.5783%

Target

2⁴⁴

0.0002

68.1818%

500

80000

0.0000

1.3376%

0.0002

68.6074%

Difference

+23

+2,468.5482

+10.9227%

+99999999500

+122192573512629700

+1,903,855.2193

+39.2156%

+1,906,323.7675

+18.9709%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12037	72223	5	16.140	3 3	-	1	3	7.258e-13	3.171e-10	5.820e-10
12037	2022217	7	20.948	84 2² × 3 × 7	2008-08-26	4	7	1.182e-11	1.191e-9	2.328e-9
12037	918212339810542718569633	24	79.603	38141245319038909968 2⁴ × 3 × 149 × 5332948171006559	2008-08-29	149	5332948171006559	10,673,370	83,090	155,190
12037	104233750878905808940981090128952728693263	42	136.259	4329722974117546271536973088350615963 13 × 1987 × 5399593 × 529511677 × 58624928115987593	2014-09-07	529511677	58624928115987593	1.485e+13	913,409	1,705,994

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

12037

72223

16.140

3
3

7.258e-13

3.171e-10

5.820e-10

12037

2022217

20.948

84
2² × 3 × 7

2008-08-26

1.182e-11

1.191e-9

2.328e-9

12037

918212339810542718569633

79.603

38141245319038909968
2⁴ × 3 × 149 × 5332948171006559

2008-08-29

149

5332948171006559

10,673,370

83,090

155,190

12037

104233750878905808940981090128952728693263

136.259

4329722974117546271536973088350615963
13 × 1987 × 5399593 × 529511677 × 58624928115987593

2014-09-07

529511677

58624928115987593

1.485e+13

913,409

1,705,994

exponent	prime factors	composite factor	digits	bits*
12037	72223 2022217	146050578391	12	37.088
12037	72223 918212339810542718569633	66316049818136826763254604159	29	95.743
12037	2022217 918212339810542718569633	1856824603174656264717727536361	31	100.551
12037	72223 2022217 918212339810542718569633	134105443315083199406708435858600503	36	116.691
12037	72223 104233750878905808940981090128952728693263	7528074189727214239144477272383352924413533649	46	152.399
12037	2022217 104233750878905808940981090128952728693263	210783263001088268239203957137300400159904224071	48	157.206
12037	72223 2022217 104233750878905808940981090128952728693263	15223399603727597997040027396327246800748762775079 833	53	173.347
12037	918212339810542718569633 104233750878905808940981090128952728693263	95708716281749316392483547181490763678075629294136 710012563482479	65	215.862
12037	72223 918212339810542718569633 104233750878905808940981090128952728693263	69123706160167808778143392280888074251216561745104 35607237372395080817	70	232.002
12037	2022217 918212339810542718569633 104233750878905808940981090128952728693263	19354379311313025734725890133071270765278706484430 1255311476087848235943	72	236.810
12037	72223 2022217 918212339810542718569633 104233750878905808940981090128952728693263	13978313370009606576391079630808063884807240184249 969562360737492663144511289	77	252.950

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-09-08	kkmrkkblmbrbk	Manual testing	100000000	10000000000	12	-	skipped known factor: 72223 skipped known factor: 2022217	-	-	0.183	-	-	12.202%
2023-03-29	-Anonymous-	T5810	100000000000	122192573512709700			918212339810542718569633 104233750878905808940981090128952728693263	65	215.862	1,903,855	4.74793e-6	3,807,710	40.553%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-09-08

kkmrkkblmbrbk

Manual testing

100000000

10000000000

skipped known factor: 72223
skipped known factor: 2022217

0.183

-

-

12.202%

2023-03-29

-Anonymous-

T5810

100000000000

122192573512709700

918212339810542718569633
104233750878905808940981090128952728693263

215.862

1,903,855

4.74793e-6

3,807,710

40.553%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2022-02-25	Kina	ftHASEE	130000000	10530000000	2	7			-	-	0.215

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2022-02-25

Kina

ftHASEE

130000000

10530000000

0.215

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26	ANONYMOUS	Manual testing	?	?	2022217	20.948	7	2.11000e-13	0.000	1.77529e-11

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26

ANONYMOUS

Manual testing

2022217

20.948

2.11000e-13

0.000

1.77529e-11

ECM factoring results:

Total ECM effort:	60.725 GHz-days
Estimated T-Level:	40.585

Digits	B1	Complete	FacMiss
20	11000	1,144.936	0.000%
25	50000	280.425	0.000%
30	250000	53.366	0.000%
35	1000000	8.221	0.027%
40	3000000	1.051	34.955%
45	11000000	0.117	88.965%
50	44000000	0.011	98.870%

ECM Summary

B1	B2	factor	curves	GHz-days
		918212339810542718569633	1	0.00000e+0
		104233750878905808940981090128952728693263	1	0.00000e+0
50000	5000000		298	0.061
250000	25000000		100	0.103
500000	50000000		10	0.021
1000000	100000000		1,736	7.144
2000000	200000000		20	0.165
3000000	300000000		4,069	50.23
11000000	2200000000		50	2.999

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29	ANONYMOUS	Manual testing			918212339810542718569633	79.603		1		1	-
2009-04-06	Matthias Wurtinger	AMD_Funzel	50000	5000000						50	0.010
2009-06-06	Rob_Dee	twopc	50000	5000000						230	0.047
2009-07-09	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-10	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-10	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-11	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-13	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-14	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-15	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-16	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-17	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-18	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-20	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-22	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-23	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-24	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-29	Rob_Dee	twopc	500000	50000000						5	0.010
2009-07-30	Rob_Dee	twopc	500000	50000000						5	0.010
2009-07-31	Matthias Wurtinger	WUR_E6600	1000000	100000000						200	0.823
2009-08-04	Rob_Dee	twopc	1000000	100000000						5	0.021
2009-08-08	Rob_Dee	twopc	2000000	200000000						5	0.041
2009-08-09	Rob_Dee	twopc	2000000	200000000						5	0.041
2009-08-11	Rob_Dee	twopc	2000000	200000000						5	0.041
2009-08-13	Rob_Dee	twopc	2000000	200000000						5	0.041
2011-04-13	James Hintz	17_051310	1000000	100000000						11	0.045
2013-06-25	BloodIce	URM2	1000000	100000000						300	1.235
2013-06-26	BloodIce	URM2	1000000	100000000						500	2.058
2013-06-27	BloodIce	URM2	1000000	100000000						470	1.934
2013-06-27	BloodIce	URM2	3000000	300000000						100	1.235
2013-07-27	BloodIce	Mjolnir4	1000000	100000000						250	1.029
2014-09-07	BloodIce	URM2			104233750878905808940981090128952728693263	136.259		1		1	-
2015-01-12	BloodIce	URM2	3000000	300000000						3969	49.00
2023-04-04	Kevin_9611		11000000	2200000000						50	2.999

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 = 100000000000, B2 = 122192573512709700 (P-1 stage 2)

B1 = 100000000000 (P-1 stage 1)

B1 = 100000000, B2 = 10000000000 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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