M3391321 Mersenne number exponent details

≡

M3391321

<<<

>>>

is 2 ^3391321 - 1

has 1020890 decimal digits

takes 0.356 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	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	2⁶⁹	8.7618	67.1642%	1150000	1001796180	8.4777	10.8683%	17.2394	70.7329%	3.5687%
PrimeNet	2⁶⁰	0.0453	63.3333%	14000	280000	0.0043	2.8459%	0.0496	64.3768%	1.0435%
GPU72	2⁶⁴	1.0495	65.6250%	18000	320000	0.0052	1.7912%	1.0548	66.2407%	0.6157%
Difference	+5	+7.7122	+1.5392%	+1132000	+1001476180	+8.4724	+9.0771%	+16.1847	+4.4922%	+4.4922%

Known prime factors (4 factors, 273.4 bits, 0.00806039% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3391321	925848886792065143	18	59.684	136502691251 31 × 977 × 4506973	-	977	4506973	0.0242	0.0375	0.0698
3391321	11726697074873703031	20	63.346	1728927617715 3² × 5 × 139 × 11483 × 24071	2017-01-31	11483	24071	0.5176	0.0019	0.0036
3391321	74445292213590044177	20	66.013	10975854573128 2³ × 1371981821641	2018-10-22	8	1371981821641	4.7058	11,384	21,261
3391321	23992342354082303190000929	26	84.311	3537315157438989584 2⁴ × 7 × 19 × 2351 × 29599 × 23887597	2022-01-06	29599	23887597	2,051,467	0.2025	0.3702

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3391321	925848886792065143 11726697074873703031	10857149432519584537473694764188548433	38	123.030
3391321	925848886792065143 74445292213590044177	68925090922862337484800221706431822311	38	125.696
3391321	11726697074873703031 74445292213590044177	872997390439224431536650959086868800487	39	129.359
3391321	925848886792065143 23992342354082303190000929	22213283460061216038367762563572535998517847	44	143.994
3391321	11726697074873703031 23992342354082303190000929	281350930902985399008916143682146526560115799	45	147.657
3391321	74445292213590044177 23992342354082303190000929	1786116937438149916330297954322474449781040433	46	150.324
3391321	925848886792065143 11726697074873703031 74445292213590044177	80826366211053379353906269081558020780927309336197 4124641	57	189.043
3391321	925848886792065143 11726697074873703031 23992342354082303190000929	26048844617444027106552676488844052332506055964194 1332431494257	63	207.341
3391321	925848886792065143 74445292213590044177 23992342354082303190000929	16536743782075637614020698361911373385162774219936 73747252926919	64	210.007
3391321	11726697074873703031 74445292213590044177 23992342354082303190000929	20945252265638329461763998795431724502511732264530 545354645652423	65	213.670
3391321	925848886792065143 11726697074873703031 74445292213590044177 23992342354082303190000929	19392138493720227642029075291069018757864848133864 421804854252454773145178751791489	83	273.354

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-10-03T23:38:18	Jocelyn Larouche	Manual testing	339132	3391321	6	-	skipped known factor: 11726697074873703031	-	-	0.077	-	-	3.844%
2022-01-06T19:15:59	Jocelyn Larouche	Manual testing	1150000	111642300			23992342354082303190000929	26	84.311	1.092	0.712	2.184	8.258%
2022-03-21T14:12:56	Jocelyn Larouche	Manual testing	1150000	1001796180		-	skipped known factor: 925848886792065143 skipped known factor: 11726697074873703031 skipped known factor: 23992342354082303190000929	-	-	8.478	-	-	10.868%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-04-24T18:52:26	LordJulius	Manual testing	2¹	2⁶²	925848886792065143	59.684	18	0.024	0.724	0.049
2022-04-24T18:52:26	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.289	-	-
2017-01-31T17:20:21	TJAOI	Manual testing	2⁶³	2⁶⁴*	11726697074873703031	63.346	20	0.047	0.724	0.095
2022-04-24T18:52:26	LordJulius	Manual testing	2⁶³	2⁶⁴	11726697074873703031	63.346	20	0.047	0.724	0.095
2022-04-24T18:52:26	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.102	-	-
2022-04-24T18:52:26	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.203	-	-
2022-04-24T18:52:26	LordJulius	Manual testing	2⁶⁶	2⁶⁷	74445292213590044177	66.013	20	0.351	0.724	0.713
2021-09-08T10:59:09	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.814	-	-
2022-01-11T12:03:34	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	17.63	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.586 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	0.586 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.129	87.895%
25	50000	0.012	98.841%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.440
50000	5000000	74445292213590044177	1	0.147

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-22T16:39:13	MarkS	laptop64	50000	5000000	74445292213590044177	66.013	1	2		1	0.147
2019-08-25T15:03:52	MarkS	laptop64	50000	5000000						3	0.440

Lucas-Lehmer results:
No L-L results for M3391321

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-05T11:46:31

kkmrkkblmbrbk

c4.xlarge

925848886792065143

11726697074873703031

842C01C36E05EE__

2017-11-21T00:57:50

Oliver Kruse

Threadripper

925848886792065143

11726697074873703031

842C01C36E05EE__

2018-10-22T17:02:28

rucio

925848886792065143

11726697074873703031

74445292213590044177

842C01C36E05EE__

2022-01-12T06:24:34

LordJulius

WhiteBox

925848886792065143

11726697074873703031

74445292213590044177

23992342354082303190000929

842C01C36E05EE5D

2022-01-14T18:09:55

GAN

LMS-11

925848886792065143

11726697074873703031

74445292213590044177

23992342354082303190000929

842C01C36E05EE5D

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 = 1150000, B2 = 1001796180 (P-1 stage 2)

B1 = 1150000, B2 = 111642300 (P-1 stage 2)

B1 = 1150000 (P-1 stage 1)

B1 = 339132, B2 = 3391321 (P-1 stage 2)

B1 = 339132 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-24T18:52:26+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