M3 252 311 Mersenne number exponent details

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M3252311

<<<

>>>

is 2 ^3252311 - 1

has 979044 decimal digits

takes 0.342 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	9FEA9FCA62134EF9	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁰	73.4710	68.5714%	8600000	22046060400	184.1588	14.1617%	257.6298	73.0223%
Target	2⁶⁴	1.0944	65.6250%	16000	1400000	0.0139	1.6551%	1.1083	66.1939%
Difference	+6	+72.3766	+2.9464%	+8584000	+22044660400	+184.1449	+12.5067%	+256.5215	+6.8283%

Known prime factors (1 factor, 130.8 bits, 0.00402099% 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
3252311	2329393423147626618196237428357394956871	40	130.775	358113572648437775199886700312085 3² × 5 × 191 × 4349 × 4591 × 1280113 × 2589649 × 629490221	2023-04-30	2589649	629490221	5.889e+10	5.5959	9.755

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-04	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.571%
2011-09-11	harlee	P4_2600	60000	1050000		-		-	-	0.017	-	-	1.488%
2014-06-11	Jocelyn Larouche	Manual testing	79735	79735		-		-	-	0.012	-	-	0.561%
2014-10-07	Jocelyn Larouche	Manual testing	99470	99470		-		-	-	0.015	-	-	0.646%
2016-01-14	Squeeky_Squirrel	P4_2600	170000	4505000	6	-		-	-	0.062	-	-	2.664%
2016-07-12	Jocelyn Larouche	Manual testing	381150	9010000	6	-		-	-	0.130	-	-	3.527%
2020-07-27	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	7.489%
2023-04-30	Sid & Andy	Hockey_Puck	8600000	22046060400			2329393423147626618196237428357394956871	40	130.775	184.2	0.683	368.3	14.162%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-18	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-04	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-21	markr	Manual testing	2¹	2⁶²		-	-	0.189	-	-
2013-01-03	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.302	-	-
2015-02-18	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.604	-	-
2015-02-18	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.149	-	-
2015-06-28	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.298	-	-
2017-03-30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.595	-	-
2019-01-14	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.191	-	-
2021-02-04	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.38	-	-
2022-01-05	TJAOI	Manual testing	2⁶⁹	2⁷⁰		-	-	36.76	-	-

ECM factoring results:

Total ECM effort:	17.467 GHz-days
Estimated T-Level:	21.781

Digits	B1	Complete	FacMiss
20	11000	3.770	2.305%
25	50000	0.356	70.032%
30	250000	0.023	97.728%
35	1000000	0.001	99.890%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	71	10.32
50000	6350000	3	0.489
50000	6750000	7	1.177
50000	38914785	7	4.103
80000	11280000	5	1.376

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-30	willreid	jing	50000	5000000						3	0.436
2011-09-24	sannerud.com	Jens2010	50000	5000000						3	0.436
2014-06-07	arnaud	Chamot18	50000	5000000						3	0.436
2016-08-25	prime_dive	erazer	50000	5000000						3	0.436
2018-12-20	Per Jessen	earth	50000	5000000						3	0.436
2020-12-31	axn	Manual testing	50000	6350000						3	0.489
2021-01-23	lycorn	colab_D_2	50000	6750000						7	1.177
2021-01-25	axn	Manual testing	80000	11280000						5	1.376
2021-04-03	Zenzoma	AM3700X_1	50000	5000000						7	1.018
2021-05-27	IanGlencross	glenx24	50000	5000000						7	1.018
2021-12-31	daveward2005	d12436	50000	5000000						7	1.018
2021-12-31	MarkS	desktop-i7	50000	5000000						21	3.053
2022-01-01	daveward2005	d12436	50000	5000000						7	1.018
2022-09-01	daveward2005	d12436	50000	5000000						7	1.018
2022-11-29	LaurV	butu	50000	38914785						7	4.103

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-21	Olli Heikkilä	v4_computers	9FEA9FCA62134EF9	0.342
1999-01-02	Olli Heikkilä	v4_computers	9FEA9FCA62134EF9	0.342
1999-11-24	ANONYMOUS	v4_computers	9FEA9FCA62134EF9	0.342

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-04-30

Naegi Makoto

5950X

2329393423147626618196237428357394956871

D01869CFC43694A9

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 = 8600000, B2 = 22046060400 (P-1 stage 2)

B1 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 8600000 (P-1 stage 1)

B1 = 4000000 (P-1 stage 1)

B1 = 381150, B2 = 9010000 (P-1 stage 2)

B1 = 170000, B2 = 4505000 (P-1 stage 2)

B1 = 381150 (P-1 stage 1)

B1 = 170000 (P-1 stage 1)

B1 = 60000, B2 = 1050000 (P-1 stage 2)

B1 = 99470 (P-1 stage 1)

B1 = 79735 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

this exponent TF target: 64

TF double-checked to: 67.9

ECM T-Level=21.78 ~= 56-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2023-09-25T11:53:03+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