M1635287 Mersenne number exponent details

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M1635287

<<<

>>>

is 2 ^1635287 - 1

has 492271 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	4AC0218428EE2348	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	18.1705	68.6567%	1000000	20000000	0.1318	5.6820%	18.3023	70.4376%	1.7809%
PrimeNet	2⁵⁷	0.0117	63.1579%	7000	120000	0.0009	2.5590%	0.0126	64.1007%	0.9428%
GPU72	2⁶¹	0.1878	65.5738%	6500	70000	0.0006	1.1191%	0.1885	65.9590%	0.3853%
Difference	+6	+17.9826	+3.0829%	+993500	+19930000	+0.1312	+4.5629%	+18.1138	+4.4786%	+4.4786%

Known prime factors (1 factor, 75.9 bits, 0.00464258% 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
1635287	71458026595457672435519	23	75.920	21848772293627257 11 × 1986252026693387	2013-11-17	11	1986252026693387	5,202.9	7,008,821	13,090,526

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T16:08:00	Axon	Manual testing	100000	100000		-		-	-	0.006	-	-	0.876%
2012-02-29T17:11:00	Axon	Manual testing	200000	200000		-		-	-	0.013	-	-	1.280%
2012-02-29T18:06:00	Axon	Manual testing	300000	300000		-		-	-	0.019	-	-	1.560%
2012-02-29T18:11:00	Axon	Manual testing	400000	400000		-		-	-	0.026	-	-	1.780%
2012-02-29T19:08:00	Axon	Manual testing	500000	500000		-		-	-	0.032	-	-	1.962%
2012-02-29T19:11:00	Axon	Manual testing	600000	600000		-		-	-	0.039	-	-	2.118%
2012-02-29T20:08:00	Axon	Manual testing	700000	700000		-		-	-	0.045	-	-	2.255%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.052	-	-	2.378%
2012-02-29T21:07:00	Axon	Manual testing	900000	900000		-		-	-	0.058	-	-	2.489%
2012-02-29T21:12:00	Axon	Manual testing	1000000	1000000		-		-	-	0.065	-	-	2.591%
2012-03-01T06:06:00	Axon	Manual testing	1000000	8000000		-		-	-	0.089	-	-	4.718%
2012-03-01T07:07:00	Axon	Manual testing	1000000	20000000		-		-	-	0.132	-	-	5.682%
2016-03-17T19:17:41	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	5.000%

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	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2010-05-02T08:49:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.094	-	-
2010-09-26T01:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.976	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.047 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	14.047 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.065	0.031%
25	50000	0.729	48.246%
30	250000	0.045	95.611%
35	1000000	0.002	99.795%

ECM Summary

B1	B2	factor	curves	GHz-days
		71458026595457672435519	1	0.00000e+0
50000	5000000		250	14.05

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-11T09:52:00	Matt	Matt	50000	5000000						3	0.169
2009-06-09T03:07:00	James Hintz	18_060209	50000	5000000						3	0.169
2010-04-28T14:10:00	unconnected	X3220--xp	50000	5000000						3	0.169
2011-09-11T19:40:00	S36049	Wolle5	50000	5000000						3	0.169
2013-03-04T13:39:00	Donna Noble	PH2x6	50000	5000000						3	0.169
2013-11-17T17:43:00	Chang Chia-Tche	exbpc13			71458026595457672435519	75.920		1		1	-
2019-11-18T17:50:27	TJAOI	Manual testing	50000	5000000						235	13.20

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	4AC0218428EE2348	0.073

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T16:01:53

Oliver Kruse

GTX-2

71458026595457672435519

73837CE6DE64F0__

2017-11-01T23:25:47

kkmrkkblmbrbk

c4.xlarge

71458026595457672435519

73837CE6DE64F0__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-11-18T17:50:27+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