M1642843 Mersenne number exponent details

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M1642843

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>>>

is 2 ^1642843 - 1

has 494546 decimal digits

takes 0.073 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	6BDF4E5E761F6F13	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	2⁶⁷	18.0869	68.6567%	1000000	20000000	0.1318	5.6850%	18.2187	70.4386%	1.7819%
PrimeNet	2⁵⁷	0.0117	63.1579%	7000	120000	0.0009	2.5613%	0.0125	64.1015%	0.9436%
GPU72	2⁶¹	0.1870	65.5738%	6500	80000	0.0007	1.1710%	0.1877	65.9769%	0.4031%
Difference	+6	+17.8999	+3.0829%	+993500	+19920000	+0.1311	+4.5140%	+18.0310	+4.4617%	+4.4617%

Known prime factors (1 factor, 73.5 bits, 0.00447377% 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
1642843	13329480955875106872767	23	73.497	4056833475832781 7 × 41 × 2852167 × 4955989	2013-11-22	2852167	4955989	1,734.2	0.1921	0.3759

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T17:06:00	Axon	Manual testing	100000	100000		-		-	-	0.006	-	-	0.877%
2012-02-29T17:11:00	Axon	Manual testing	200000	200000		-		-	-	0.013	-	-	1.281%
2012-02-29T18:06:00	Axon	Manual testing	300000	300000		-		-	-	0.019	-	-	1.561%
2012-02-29T18:11:00	Axon	Manual testing	400000	400000		-		-	-	0.026	-	-	1.781%
2012-02-29T19:09:00	Axon	Manual testing	500000	500000		-		-	-	0.032	-	-	1.963%
2012-02-29T19:12:00	Axon	Manual testing	600000	600000		-		-	-	0.039	-	-	2.119%
2012-02-29T20:08:00	Axon	Manual testing	700000	700000		-		-	-	0.045	-	-	2.257%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.052	-	-	2.379%
2012-02-29T21:08:00	Axon	Manual testing	900000	900000		-		-	-	0.058	-	-	2.491%
2012-02-29T21:12:00	Axon	Manual testing	1000000	1000000		-		-	-	0.065	-	-	2.593%
2012-03-01T06:07:00	Axon	Manual testing	1000000	8000000		-		-	-	0.089	-	-	4.720%
2012-03-01T07:08:00	Axon	Manual testing	1000000	20000000		-		-	-	0.132	-	-	5.685%
2016-03-17T19:17:47	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	5.003%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2010-04-30T16:30:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.093	-	-
2010-07-30T00:04:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.971	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.941 GHz-days
Estimated T-Level:	24.429

Digits	B1	Curves	Complete	FacMiss
20	11000	248 / 100	2.480	8.270%
25	50000	248 / 280	0.886	41.177%

New Calculation Method

Total ECM effort:	13.941 GHz-days
Estimated T-Level:	24.429

Digits	B1	Complete	FacMiss
20	11000	8.000	0.034%
25	50000	0.723	48.528%
30	250000	0.045	95.645%
35	1000000	0.002	99.796%

ECM Summary

B1	B2	factor	curves	GHz-days
		13329480955875106872767	1	0.00000e+0
50000	5000000		248	13.94

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-10T05:20:00	paulie	iMac3.4	50000	5000000						3	0.169
2009-06-04T06:57:00	James Hintz	15_061809	50000	5000000						3	0.169
2010-06-14T05:22:00	Dougal	dougal	50000	5000000						3	0.169
2011-09-19T20:54:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.169
2013-03-09T17:15:00	Donna Noble	PH2x6	50000	5000000						3	0.169
2013-11-22T17:20:00	Chang Chia-Tche	exbpc13			13329480955875106872767	73.497		1		1	-
2019-11-18T17:50:46	TJAOI	Manual testing	50000	5000000						233	13.10

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	6BDF4E5E761F6F13	0.073

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T17:20:49

Oliver Kruse

GTX-2

13329480955875106872767

C76A0611B59F8A__

2017-11-02T03:20:45

kkmrkkblmbrbk

c4.xlarge

13329480955875106872767

C76A0611B59F8A__

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-11-18T17:50:46+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