M10 331 Mersenne number exponent details

is 2 ¹⁰³³¹ - 1

has 3110 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	2,876.1899	79.1045%	100000000000	121968084023145360	1,263,336.2856	40.3569%	1,266,212.4755	87.5373%
Target	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.2765%	0.0002	68.5880%
Difference	+23	+2,876.1896	+10.9227%	+99999999500	+121968084023135360	+1,263,336.2856	+39.0804%	+1,266,212.4753	+18.9493%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10331	20663	5	14.335	1 1	-	1	1	2.113e-13	1.901e-10	3.869e-10
10331	268607	6	18.035	13 13	2008-08-26	1	13	3.390e-12	3.144e-10	3.869e-10
10331	4049753	7	21.949	196 2² × 7²	2008-08-26	49	49	2.819e-11	9.315e-9	1.896e-8
10331	97752764881359148153	20	66.406	4731040793793396 2² × 3 × 229 × 491 × 3506375897	2008-08-29	491	3506375897	1,985.6	0.0363	0.0678
10331	437845093053330662637637679407121	33	108.432	21190837917594166229679492760 2³ × 5 × 7 × 11 × 547 × 623681 × 20167291380173521	2009-03-05	623681	20167291380173521	1.450e+13	208,888	390,145

exponent	prime factors	composite factor	digits	bits*
10331	20663 268607	5550226441	10	32.370
10331	20663 4049753	83680046239	11	36.284
10331	268607 4049753	1087792004071	13	39.985
10331	20663 268607 4049753	22477046180119073	17	54.319
10331	20663 97752764881359148153	2019865380743524078285439	25	80.741
10331	268607 97752764881359148153	26257076916487236707932871	26	84.441
10331	4049753 97752764881359148153	395874552836578854310056209	27	88.355
10331	20663 268607 97752764881359148153	542549980325375772096016913473	30	98.776
10331	20663 4049753 97752764881359148153	8179955885262228866608691446567	31	102.690
10331	268607 4049753 97752764881359148153	106334676013774936319661268130863	33	106.390
10331	20663 268607 4049753 97752764881359148153	2197193410472631509173160783388022169	37	120.725
10331	20663 437845093053330662637637679407121	9047193157760971482081507369589341223	37	122.767
10331	268607 437845093053330662637637679407121	117608256909775989299107944152508550447	39	126.467
10331	4049753 437845093053330662637637679407121	1773164479128005011008761105092026491113	40	130.382
10331	20663 268607 437845093053330662637637679407121	2430139412526701266887467450023284177886361	43	140.802
10331	20663 4049753 437845093053330662637637679407121	36638897632221967542474030714516543385867919	44	144.716
10331	268607 4049753 437845093053330662637637679407121	476284391245136041992030294155453959698389591	45	148.417
10331	20663 268607 4049753 437845093053330662637637679407121	9841464376298246035681321968134145169247824118833	49	162.751
10331	97752764881359148153 437845093053330662637637679407121	42800568435699049915235144214335328270959874642197 513	53	174.838
10331	20663 97752764881359148153 437845093053330662637637679407121	88438814558684946839850378490081088806284388973172 7211119	57	189.173
10331	268607 97752764881359148153 437845093053330662637637679407121	11496532285807814700581566381979969520877719048016 747374391	59	192.873
10331	4049753 97752764881359148153 437845093053330662637637679407121	17333173042417753449137327098743713867130456521186 3304864289	60	196.787
10331	20663 268607 97752764881359148153 437845093053330662637637679407121	23755284662164687515811690615085211020989630868917 0050997041233	63	207.208
10331	20663 4049753 97752764881359148153 437845093053330662637637679407121	35815535457547803951952458984134135963651662309727 31468410803607	64	211.122
10331	268607 4049753 97752764881359148153 437845093053330662637637679407121	46558116114047055007124300200122527507083105347862 966729682075423	65	214.822
10331	20663 268607 4049753 97752764881359148153 437845093053330662637637679407121	96203035326455429761220941503513178587885820580289 2481535420724465449	69	229.157

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-09-07	kkmrkkblmbrbk	Manual testing	100000000	10000000000	12	-	skipped known factor: 20663 skipped known factor: 268607 skipped known factor: 4049753 skipped known factor: 97752764881359148153	-	-	0.122	-	-	12.067%
2021-08-01	ViliamF	3	250000000	40250000000		-	skipped known factor: 20663 skipped known factor: 268607 skipped known factor: 4049753 skipped known factor: 97752764881359148153	-	-	0.462	-	-	14.543%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 20663 skipped known factor: 268607 skipped known factor: 4049753	-	-	0.076	-	-	7.643%
2022-03-28	-Anonymous-	DL560G8	100000000000	121968084023145360			437845093053330662637637679407121	33	108.432	1,263,336	2.70902e-6	2,526,673	40.357%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	268607	18.035	6	9.51180e-15	0.000	1.61340e-12
2008-08-26	ANONYMOUS	Manual testing	?	?	4049753	21.949	7	1.14727e-12	0.000	1.94601e-10

ECM factoring results:

Total ECM effort:	38.073 GHz-days
Estimated T-Level:	40.561

Digits	B1	Complete	FacMiss
20	11000	1,037.450	0.000%
25	50000	260.368	0.000%
30	250000	50.424	0.000%
35	1000000	7.854	0.039%
40	3000000	1.009	36.464%
45	11000000	0.112	89.383%
50	44000000	0.011	98.924%

ECM Summary

B1	B2	factor	curves	GHz-days
		97752764881359148153	1	0.00000e+0
		437845093053330662637637679407121	1	0.00000e+0
50000	5000000		355	0.049
250000	25000000		2	0.001
350000	35000000		6	0.006
400000	40000000		1	0.001
950000	95000000		5	0.013
1000000	100000000		969	2.651
3000000	300000000		4,301	35.30
10000000	1000000000		2	0.055

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29	ANONYMOUS	Manual testing			97752764881359148153	66.406		1		1	-
2009-03-05	ANONYMOUS	Manual testing			437845093053330662637637679407121	108.432		1		1	-
2009-04-02	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.007
2009-04-24	Rob_Dee	twopc	50000	5000000						90	0.012
2009-04-24	Rob_Dee	twopc	50000	5000000						80	0.011
2009-04-24	Rob_Dee	twopc	50000	5000000						60	0.008
2009-07-11	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-12	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-12	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-13	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-26	Rob_Dee	twopc	50000	5000000						19	0.003
2009-07-28	Rob_Dee	twopc	50000	5000000						19	0.003
2009-07-28	Rob_Dee	twopc	250000	25000000						2	0.001
2009-07-28	Rob_Dee	twopc	50000	5000000						19	0.003
2009-07-29	Rob_Dee	twopc	950000	95000000						1	0.003
2009-07-30	Rob_Dee	twopc	950000	95000000						1	0.003
2009-07-31	Rob_Dee	twopc	950000	95000000						1	0.003
2009-08-01	Rob_Dee	twopc	950000	95000000						1	0.003
2009-08-02	Rob_Dee	twopc	400000	40000000						1	0.001
2009-08-02	Rob_Dee	twopc	350000	35000000						3	0.003
2009-08-04	Rob_Dee	twopc	950000	95000000						1	0.003
2009-08-05	Rob_Dee	twopc	350000	35000000						3	0.003
2009-08-08	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-09	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-11	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-13	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-14	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-14	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-15	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-17	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-18	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-19	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-20	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-21	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-21	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-23	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-24	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-24	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-25	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-26	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-27	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-28	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-29	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-30	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-30	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-31	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-01	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-02	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-03	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-04	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-05	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-05	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-05	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-06	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-08	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-11	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-12	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-12	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-14	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-15	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-16	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-17	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-18	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-19	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-20	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-21	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-22	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-23	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-24	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-25	Rob_Dee	twopc	1000000	100000000						1	0.003
2010-01-06	Rob_Dee	twopc	1000000	100000000						1	0.003
2010-01-07	Rob_Dee	twopc	1000000	100000000						10	0.027
2010-01-08	Rob_Dee	twopc	10000000	1000000000						1	0.027
2010-01-09	Rob_Dee	twopc	1000000	100000000						10	0.027
2010-01-09	Rob_Dee	twopc	10000000	1000000000						1	0.027
2010-01-30	Matthias Wurtinger	WUR_E6600	1000000	100000000						100	0.274
2010-02-13	Matthias Wurtinger	AMD_Funzel	1000000	100000000						100	0.274
2010-02-16	Matthias Wurtinger	WUR_E6600	1000000	100000000						300	0.821
2010-02-20	Matthias Wurtinger	WUR_E6600	1000000	100000000						400	1.094
2010-03-15	Matthias Wurtinger	WUR_E6600	3000000	300000000						200	1.641
2011-01-04	James Hintz	home2	3000000	300000000						3	0.025
2011-04-22	James Hintz	17_051310	3000000	300000000						11	0.090
2016-12-15	James Hintz	alek_07_13_2016	3000000	300000000						100	0.821
2019-02-25	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-02-27	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-02-28	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-03-11	Alex	home	3000000	300000000						1000	8.207
2019-04-26	James Hintz	lappy_3_1_2018	3000000	300000000						2978	24.44

Lucas-Lehmer results:
No L-L results for M10331

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

20663

268607

4049753

97752764881359148153

437845093053330662637637679407121

BD0A62C83F03EB94

2017-09-21

Oliver Kruse

Manual testing

20663

268607

4049753

97752764881359148153

437845093053330662637637679407121

BD0A62C83F03EB94

2017-10-02

kkmrkkblmbrbk

Manual testing

20663

268607

4049753

97752764881359148153

437845093053330662637637679407121

BD0A62C83F03EB__

2017-10-12

kkmrkkblmbrbk

Manual testing

20663

268607

4049753

97752764881359148153

437845093053330662637637679407121

BD0A62C83F03EB__

2020-04-17

Oliver Kruse

Manual testing

20663

268607

4049753

97752764881359148153

437845093053330662637637679407121

9C9EA4892276FD__

2022-05-12

Jorge Coveiro

Manual testing

20663

9C9EA4892276FD48

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 = 121968084023145360 (P-1 stage 2)

B1 = 100000000000 (P-1 stage 1)

B1 = 250000000, B2 = 40250000000 (P-1 stage 2)

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

B1 = 400000000 (P-1 stage 1)

B1 = 250000000 (P-1 stage 1)

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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=40.56 ~= 118-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2023-03-25T13:08:14+00:00

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