M662617 Mersenne number exponent details

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M662617

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is 2 ⁶⁶²⁶¹⁷ - 1

has 199468 decimal digits

takes 0.010 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	44.8433	70.1493%	1000000	30000000	0.0568	5.5227%	44.9001	71.7978%	1.6486%
PrimeNet	2⁴⁰	0.0000	50.0000%	6000	240000	0.0004	20.9982%	0.0004	60.4991%	10.4991%
GPU72	2⁴⁴	0.0000	54.5455%	11000	400000	0.0007	15.9942%	0.0007	61.8155%	7.2701%
Difference	+23	+44.8433	+15.6038%	+989000	+29600000	+0.0561	-10.4715%	+44.8994	+9.9823%	+9.9823%

Known prime factors (2 factors, 122.9 bits, 0.01855279% 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
662617	528302374238927737	18	58.874	398648370204 2² × 3³ × 7 × 527312659	2014-04-03	27	527312659	0.0590	0.6330	1.1822
662617	19227669819771746407	20	64.060	14508886596459 3 × 223 × 21687423911	2007-11-24	223	21687423911	6.8106	26.033	48.622

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
662617	528302374238927737 19227669819771746407	10158023616867589402765331443562390959	38	122.934

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	-	-	0.192%
2002-01-22T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.414%
2002-03-10T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.001	-	-	0.752%
2002-05-05T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.227%
2002-07-06T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.005	-	-	1.848%
2002-10-12T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.608%
2003-06-06T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.497%
unknown			1000000	30000000		-		-	-	0.057	-	-	5.523%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-02-01T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07T09:02:31	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.014	-	-
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.029	-	-
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.058	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.522 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	323 / 100	3.230	3.892%
25	50000	323 / 280	1.154	31.486%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	8.522 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.731	0.000%
25	50000	1.613	19.937%
30	250000	0.131	87.717%
35	1000000	0.009	99.131%

ECM Summary

B1	B2	factor	curves	GHz-days
		528302374238927737	1	0.00000e+0
		19227669819771746407	1	0.00000e+0
50000	5000000		279	4.765
250000	25000000		44	3.757

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-27T00:09:00	Chad Davis	Bayes	50000	5000000						1	0.017
2007-11-23T04:00:00	Andi47	Core2Duo	50000	5000000						1	0.017
2007-11-24T03:38:00	James Heinrich	WHS			19227669819771746407	64.060		1		1	-
2014-04-03T12:52:00	Richard B. Woods	Puttputt	50000	5000000						7	0.120
2014-04-03T12:52:00	Richard B. Woods	Puttputt			528302374238927737	58.874		1		1	-
2015-10-09T10:36:33	TJAOI	Manual testing	50000	5000000						89	1.520
2016-05-06T13:28:17	TJAOI	Manual testing	50000	5000000						90	1.537
2017-03-10T18:27:02	TJAOI	Manual testing	50000	5000000						91	1.554
2019-08-19T13:16:21	TJAOI	Manual testing	250000	25000000						44	3.757

Lucas-Lehmer results:
No L-L results for M662617

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T14:20:53

Oliver Kruse

GTX-3

528302374238927737

19227669819771746407

D656CF7ED515B1__

2017-09-28T09:44:52

Oliver Kruse

Manual testing

528302374238927737

19227669819771746407

D656CF7ED515B1__

2017-11-09T02:25:24

kkmrkkblmbrbk

c4.large

528302374238927737

19227669819771746407

D656CF7ED515B1__

2020-04-19T23:51:30

Oliver Kruse

AddPrpType5

528302374238927737

19227669819771746407

2546EDBCD2C5C7__

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 = 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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T09:02:31+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