M600517 Mersenne number exponent details

is 2 ⁶⁰⁰⁵¹⁷ - 1

has 180774 decimal digits

takes 0.009 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	49.4806	70.1493%	10000000	200000000	0.4484	8.9404%	49.9289	72.8180%	2.6688%
PrimeNet	2⁴⁰	0.0000	50.0000%	6000	220000	0.0004	20.5190%	0.0004	60.2595%	10.2595%
GPU72	2⁴⁴	0.0000	54.5455%	10000	360000	0.0006	15.4297%	0.0006	61.5590%	7.0135%
Difference	+23	+49.4806	+15.6038%	+9990000	+199640000	+0.4477	-6.4894%	+49.9283	+11.2590%	+11.2590%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
600517	6893595841357444351644119	25	82.512	5739717477904409327 35521 × 877073 × 184233919	2011-03-02	877073	184233919	3,024,484	0.2394	0.4130
600517	1539328503300812094923774591	28	90.314	1281669380967409827635 5 × 11 × 79 × 10087219 × 29242518857	2020-07-31	10087219	29242518857	502,049,492	35.312	65.560

exponent	prime factors	composite factor	digits	bits*
600517	6893595841357444351644119 1539328503300812094923774591	10611508568837457308318700605799670819920492206780 329	53	172.826

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.187%
2002-01-22T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.404%
2002-03-10T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.001	-	-	0.735%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.203%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.005	-	-	1.816%
2002-09-29T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.568%
2003-05-04T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.449%
2016-03-17T18:48:47	alpertron	Manual testing	1000000	30000000	12	-		-	-	0.057	-	-	5.461%
unknown			10000000	200000000		-	MISSED FACTOR!	-	-	0.448	-	-	8.940%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.016	-	-
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.032	-	-
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.064	-	-
2008-10-11T06:36:00	Sturle Sunde	bruch.ifi	2⁵⁸	2⁵⁹		-	-	0.064	-	-
2008-10-11T07:20:00	Sturle Sunde	bruch.ifi	2⁵⁹	2⁶⁰		-	-	0.128	-	-
2010-08-13T06:51:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.256	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.614 GHz-days
Estimated T-Level:	26.117

Digits	B1	Curves	Complete	FacMiss
20	11000	429 / 100	4.290	1.341%
25	50000	429 / 280	1.532	21.548%
30	250000	143 / 640	0.223	79.963%

New Calculation Method

Total ECM effort:	17.614 GHz-days
Estimated T-Level:	26.117

Digits	B1	Complete	FacMiss
20	11000	21.142	0.000%
25	50000	2.598	7.444%
30	250000	0.242	78.502%
35	1000000	0.018	98.192%
40	3000000	0.001	99.885%

ECM Summary

B1	B2	factor	curves	GHz-days
		6893595841357444351644119	1	0.00000e+0
50000	5000000		286	4.846
250000	25000000		43	3.643
250000	25000000	1539328503300812094923774591	63	5.337
250000	40000000		37	3.789

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-22T16:56:00	drew	messier	50000	5000000						1	0.017
2007-10-09T14:27:00	Chad Davis	Bayes	50000	5000000						1	0.017
2008-01-19T21:03:00	Steve Scott	Celeron	50000	5000000						3	0.051
2008-09-09T12:17:00	Sturle Sunde	v17	50000	5000000						3	0.051
2008-11-15T18:34:00	Sturle Sunde	v23	50000	5000000						3	0.051
2009-01-28T01:36:00	Sturle Sunde	v21	50000	5000000						3	0.051
2009-03-19T12:29:00	James Heinrich	WHS	50000	5000000						3	0.051
2009-06-03T04:12:00	Sturle Sunde	TOR-ST-0020	50000	5000000						3	0.051
2009-07-09T12:48:00	Architects Cubed	m1_48	50000	5000000						3	0.051
2009-07-30T11:11:00	linded	KCPB8P0-NET214	50000	5000000						3	0.051
2009-09-15T15:29:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-10-14T00:40:00	linded	KCPB8P0-NET214	50000	5000000						3	0.051
2009-10-31T02:08:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-11-19T06:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-12-11T18:58:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-01-03T05:58:00	James Hintz	13_122109	50000	5000000						3	0.051
2010-01-21T23:48:00	James Hintz	02_122109	50000	5000000						3	0.051
2010-02-06T00:39:00	James Hintz	17_012210	50000	5000000						3	0.051
2010-02-23T23:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-03-17T04:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-04-03T20:42:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-04-22T02:21:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-05-09T17:41:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-05-28T16:29:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-06-19T19:00:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-07-18T04:15:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-08-14T17:22:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-09-04T16:45:00	Sturle Sunde	TOR-ST-0027	50000	5000000						3	0.051
2010-09-21T15:51:00	LordJulius	rambus	50000	5000000						3	0.051
2010-10-09T09:20:00	josibo	Ziben	50000	5000000						3	0.051
2010-10-23T23:25:00	Sturle Sunde	TOR-ST-0017	50000	5000000						3	0.051
2010-11-07T22:57:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.051
2010-11-27T04:47:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-12-09T21:47:00	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.051
2010-12-27T06:06:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-01-12T21:08:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2011-01-25T20:27:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-02-11T05:20:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-02-25T00:20:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-02-27T00:14:00	alpertron	Manual testing	50000	5000000						173	2.931
2011-03-02T19:29:00	alpertron	Manual testing			6893595841357444351644119	82.512		1		1	-
2018-07-27T12:40:13	TJAOI	Manual testing	250000	25000000						43	3.643
2020-07-31T11:05:45	nordi	sweet16	250000	25000000	1539328503300812094923774591	90.314	63	2	3588669140325542	63	5.337
2022-05-05T09:28:57	TJAOI	Manual testing	250000	40000000						37	3.789

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-07-06T00:00:00	ANONYMOUS	v4_computers	6E0AF0D81EBEE665	0.009

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T12:14:05

Oliver Kruse

GTX-3

6893595841357444351644119

DF3A5B82E6C640__

2017-09-28T09:43:54

Oliver Kruse

Manual testing

6893595841357444351644119

DF3A5B82E6C640__

2017-11-09T03:48:28

kkmrkkblmbrbk

c4.large

6893595841357444351644119

DF3A5B82E6C640__

2020-04-19T13:10:16

Oliver Kruse

AddPrpType5

6893595841357444351644119

6832533E63C516__

2020-07-31T11:27:45

CrypticClue

Manual testing

6893595841357444351644119

1539328503300812094923774591

6832533E63C516F0

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 = 10000000, B2 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-05T09:28:57+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