M3234893 Mersenne number exponent details

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M3234893

<<<

>>>

is 2 ^3234893 - 1

has 973800 decimal digits

takes 0.275 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	84EDB23F39539A37	double-checked
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	36.9059	68.1159%	4000000	150000000	1.4753	8.1070%	38.3813	70.7008%	2.5848%
PrimeNet	2⁶⁰	0.0475	63.3333%	14000	260000	0.0034	2.7685%	0.0509	64.3485%	1.0151%
GPU72	2⁶⁴	1.1003	65.6250%	16000	280000	0.0037	1.6534%	1.1040	66.1933%	0.5683%
Difference	+5	+35.8057	+2.4909%	+3984000	+149720000	+1.4716	+6.4537%	+37.2772	+4.5074%	+4.5074%

Known prime factors (1 factor, 117.3 bits, 0.00362659% 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
3234893	206900079817108133950117344712918193	36	117.316	31979431748918454791258527672 2³ × 7 × 17² × 37 × 25463 × 179351 × 287921 × 40615933	2020-04-28	287921	40615933	4.378e+10	0.3067	0.5101

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	durandal	15000	191250		-		-	-	0.003	-	-	0.669%
2011-09-28T20:03:00	markr	tiny	200000	4500000		-		-	-	0.054	-	-	3.061%
2018-07-24T12:57:29	Jocelyn Larouche	low 4M	400000	1042180		-		-	-	0.054	-	-	2.259%
2018-07-27T18:51:11	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.074	-	-	3.286%
2020-04-28T09:05:57	mikr	MSI	4000000	150000000	12		206900079817108133950117344712918193	36	117.316	1.475	0.551	2.951	8.107%
2021-01-18T13:43:04	Jocelyn Larouche	Manual testing	420000	3234893	6	-		-	-	0.071	-	-	3.138%
2021-12-25T10:08:08	Jocelyn Larouche	Manual testing	3234893	116701200		-	skipped known factor: 206900079817108133950117344712918193	-	-	1.162	-	-	7.678%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-05T22:53:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-07-25T20:43:00	Carsten Kossendey	Manual testing	2⁶¹	2⁶³		-	-	0.398	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.607	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.155	-	-
2015-06-24T21:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.310	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.310	-	-
2021-02-22T09:03:46	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.620	-	-
2017-03-26T03:14:46	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.620	-	-
2018-11-26T14:19:37	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.240	-	-
2021-12-08T12:48:18	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.48	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.765 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.765 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.765

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-13T17:36:00	GrunwalderGIMP	GLaptopUbuntu	50000	5000000						3	0.353
2011-09-13T22:44:00	sannerud.com	JimEmcLW7	50000	5000000						3	0.353
2014-05-22T14:15:00	Lukasz Wrobel	i-3	50000	5000000						3	0.353
2016-08-16T19:50:24	Bruce	desk	50000	5000000						3	0.353
2018-10-31T05:17:35	tottenhoff	2011pc	50000	5000000						3	0.353

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-21T00:00:00	ANONYMOUS	v4_computers	84EDB23F39539A37	0.275
1999-05-30T00:00:00	ANONYMOUS	v4_computers	84EDB23F39539A37	0.275

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-04-28T11:07:08

mikr

MSI

206900079817108133950117344712918193

D444C10FA4FE65EC

2020-04-28T11:58:53

ANONYMOUS

dory

206900079817108133950117344712918193

D444C10FA4FE65EC

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 = 3234893, B2 = 116701200 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3234893 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 420000, B2 = 3234893 (P-1 stage 2)

B1 = 400000, B2 = 1042180 (P-1 stage 2)

B1 = 200000, B2 = 4500000 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 200000 (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

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2021-12-25T10:08:08+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