M3212101 Mersenne number exponent details

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M3212101

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>>>

is 2 ^3212101 - 1

has 966939 decimal digits

takes 0.273 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	BDFE13E5C22EEB1B	double-checked
PRP	E4E0C6630E304073	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	18.5564	67.6471%	4000000	150000000	1.4753	8.7641%	20.0317	70.4825%	2.8354%
PrimeNet	2⁶⁰	0.0478	63.3333%	13000	240000	0.0031	2.6593%	0.0509	64.3084%	0.9751%
GPU72	2⁶⁴	1.1081	65.6250%	16000	260000	0.0036	1.6169%	1.1117	66.1808%	0.5558%
Difference	+4	+17.4483	+2.0221%	+3984000	+149740000	+1.4717	+7.1472%	+18.9200	+4.3017%	+4.3017%

Known prime factors (1 factor, 83.5 bits, 0.00259812% 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
3212101	13249173351261001877129609	26	83.454	2062384301001276404 2² × 19 × 135971089 × 199576511	2020-12-23	135971089	199576511	995,842	17.208	34.151

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:38:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.783%
2011-09-25T13:11:00	harlee	P4_2600	55000	852500		-		-	-	0.012	-	-	1.786%
2013-09-03T16:48:00	Squeeky_Squirrel	T7500_2200	115000	2587500		-		-	-	0.031	-	-	2.743%
2016-11-19T23:34:00	Squeeky_Squirrel	P4_2600	200000	5600000	12	-		-	-	0.061	-	-	3.571%
2018-07-23T17:58:37	Jocelyn Larouche	low 4M	400000	400000		-		-	-	0.049	-	-	1.751%
2018-08-05T20:06:25	Jocelyn Larouche	low 4M	400000	2576000		-		-	-	0.064	-	-	3.271%
2018-08-06T19:37:25	Jocelyn Larouche	low 4M	400000	3376000		-		-	-	0.069	-	-	3.498%
2018-08-07T17:09:26	Jocelyn Larouche	low 4M	400000	3776000		-		-	-	0.072	-	-	3.593%
2020-01-31T08:03:27	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.764%
2021-01-17T23:14:13	Jocelyn Larouche	Manual testing	420000	3212101	6	-		-	-	0.071	-	-	3.474%
2021-01-17T23:14:14	Jocelyn Larouche	Manual testing	420000	6424202	6	-		-	-	0.092	-	-	4.071%
2022-01-06T11:35:03	Jocelyn Larouche	Manual testing	1231815	116447100		-		-	-	0.927	-	-	7.644%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-07T22:18:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-09-02T01:47:00	markr	Manual testing	2⁶¹	2⁶²		-	-	0.096	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.306	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.611	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.163	-	-
2015-06-21T21:40:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.326	-	-
2021-01-17T23:14:14	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.326	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.653	-	-
2017-03-17T19:55:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.653	-	-
2019-01-07T14:44:18	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.306	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.468 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	2.468 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.808	44.589%
25	50000	0.075	92.799%
30	250000	0.005	99.530%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.763
50000	5000000	13249173351261001877129609	6	0.705

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-15T05:09:00	Marzbug	Xeon	50000	5000000						3	0.353
2011-09-13T12:38:00	Lukasz Wrobel	i-4	50000	5000000						3	0.353
2014-05-03T10:16:00	bunddog	debian	50000	5000000						3	0.353
2016-07-30T13:33:40	Dennis Schreiber	z400	50000	5000000						3	0.353
2018-10-16T04:58:17	arnaud	attax05	50000	5000000						3	0.353
2020-12-23T22:21:56	Zenzoma	AM3700X_1	50000	5000000	13249173351261001877129609	83.454	6	2	2623567303414458	6	0.705

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-01T00:00:00	schaz	v4_computers	BDFE13E5C22EEB1B	0.273
1999-06-06T00:00:00	ANONYMOUS	v4_computers	BDFE13E5C22EEB1B	0.273

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-12-25T02:23:04

Niels_Mache_Nextcloud

conf4-a

13249173351261001877129609

E4E0C6630E304073

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1231815, B2 = 116447100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1231815 (P-1 stage 1)

B1 = 420000, B2 = 6424202 (P-1 stage 2)

B1 = 400000, B2 = 3776000 (P-1 stage 2)

B1 = 420000, B2 = 3212101 (P-1 stage 2)

B1 = 400000, B2 = 3376000 (P-1 stage 2)

B1 = 400000, B2 = 2576000 (P-1 stage 2)

B1 = 200000, B2 = 5600000 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 115000, B2 = 2587500 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 55000, B2 = 852500 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-06T11:35:03+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