M1687729 Mersenne number exponent details

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M1687729

<<<

>>>

is 2 ^1687729 - 1

has 508058 decimal digits

takes 0.079 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	4D571E5185A3B75D	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	17.6059	68.6567%	1000000	20000000	0.1389	5.7024%	17.7447	70.4440%	1.7873%
PrimeNet	2⁵⁷	0.0114	63.1579%	8000	130000	0.0010	2.7275%	0.0124	64.1628%	1.0049%
GPU72	2⁶¹	0.1820	65.5738%	7000	90000	0.0008	1.2567%	0.1828	66.0064%	0.4326%
Difference	+6	+17.4239	+3.0829%	+993000	+19910000	+0.1381	+4.4458%	+17.5619	+4.4376%	+4.4376%

Known prime factors (1 factor, 75.9 bits, 0.00449948% 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
1687729	72432107366777357512321	23	75.939	21458453154143040 2⁶ × 3³ × 5 × 7 × 109 × 3255068497	2014-08-26	109	3255068497	4,946.0	12.102	22.603

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-25T02:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.570%
2012-02-29T17:11:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.882%
2012-02-29T17:15:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.286%
2012-02-29T18:10:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.568%
2012-02-29T18:13:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.788%
2012-02-29T19:11:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.971%
2012-02-29T19:14:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	2.128%
2012-02-29T20:10:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.265%
2012-02-29T20:13:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.389%
2012-02-29T21:12:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.500%
2012-02-29T21:14:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.603%
2012-03-01T06:09:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.735%
2012-03-01T07:10:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.702%
2016-03-17T19:18:44	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.019%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	dakruger	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2022-03-08T23:06:22	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.068	-	-
2010-04-26T14:20:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.091	-	-
2010-09-26T01:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.946	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.908 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.908 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	14.85
50000	5000000	72432107366777357512321	1	0.059

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-15T22:20:00	James Heinrich	Q6600	50000	5000000						3	0.178
2009-06-12T04:19:00	Lupo	yorick	50000	5000000						3	0.178
2010-07-01T04:49:00	James Hintz	12_052810	50000	5000000						3	0.178
2011-11-09T11:05:00	OS1	L3	50000	5000000						3	0.178
2013-04-07T12:21:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2013-12-26T16:11:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-08-26T20:29:00	Chang Chia-Tche	exbpc13	50000	5000000	72432107366777357512321	75.939	1	2		1	0.059
2020-01-27T11:16:38	TJAOI	Manual testing	50000	5000000						232	13.78

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	dakruger	v4_computers	4D571E5185A3B75D	0.079

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T01:16:42

Oliver Kruse

GTX-2

72432107366777357512321

E70EB8DD90E456__

2017-11-03T11:50:55

Chang Chia-Tche

exbpc13

72432107366777357512321

E70EB8DD90E456__

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)

B1 = 50000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-08T23:06:22+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