M1002647 Mersenne number exponent details

≡

M1002647

<<<

>>>

is 2 ^1002647 - 1

has 301827 decimal digits

takes 0.030 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	B5D6BD5740A5B9DA	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	29.6355	70.1493%	10000000	1110000000	3.0054	11.7613%	32.6409	73.6601%	3.5108%
PrimeNet	2⁵⁶	0.0096	64.2857%	4500	60000	0.0003	1.9398%	0.0099	64.9785%	0.6928%
GPU72	2⁶⁰	0.1532	66.6667%	4500	16000	0.0002	0.5774%	0.1534	66.8591%	0.1925%
Difference	+7	+29.4823	+3.4826%	+9995500	+1109984000	+3.0052	+11.1840%	+32.4875	+6.8010%	+6.8010%

Known prime factors (2 factors, 137.9 bits, 0.01375136% 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
1002647	325041907948871839553	21	68.139	162091896723808 2⁵ × 5065371772619	2016-12-30	32	5065371772619	100.85	11,860	22,152
1002647	984829087269388376423	21	69.738	491114563385413 11 × 8783 × 5083317601	2009-10-09	8783	5083317601	193.74	11.903	22.230

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1002647	325041907948871839553 984829087269388376423	320110725529588008278772281062688024058919	42	137.878

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-10-22T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.004	-	-	1.702%
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.223%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	60000	60000		-		-	-	0.003	-	-	0.580%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	78000	78000		-		-	-	0.003	-	-	0.687%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	98000	98000		-		-	-	0.004	-	-	0.790%
2009-06-05T23:23:00	Rob_Dee	twopc	200000	400000		-		-	-	0.009	-	-	1.613%
2009-06-06T15:36:00	Rob_Dee	twopc	400000	600000		-		-	-	0.018	-	-	1.961%
2009-06-06T19:50:00	Rob_Dee	twopc	600000	800000		-		-	-	0.026	-	-	2.215%
2016-03-17T18:58:55	alpertron	Manual testing	300000	10000000	12	-		-	-	0.036	-	-	4.066%
2021-05-25T07:43:34	ViliamF	3	10000000	1110000000		-		-	-	3.005	-	-	11.761%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-22T00:00:00	ANONYMOUS	v4_computers	2⁵⁶	2⁵⁷		-	-	0.010	-	-
2002-12-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.038	-	-
2022-03-07T17:30:11	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.115	-	-
2009-02-17T03:54:00	Sturle Sunde	zumthor.ifi	2⁶⁰	2⁶¹		-	-	0.153	-	-
2022-04-11T22:45:03	LordJulius	Manual testing	2¹	2⁶¹		-	-	0.306	-	-
2022-04-11T22:45:03	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.306	-	-
2022-04-11T22:45:03	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.979	-	-
2022-04-11T22:45:03	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	1.958	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.353 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:	17.353 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
		984829087269388376423	1	0.00000e+0
50000	5000000		256	8.902
50000	5000000	325041907948871839553	23	0.800
250000	25000000		44	7.651

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-17T16:20:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-02-06T19:50:00	Team_Bundu	bundu4	50000	5000000						3	0.104
2008-11-23T21:54:00	Sturle Sunde	v21	50000	5000000						3	0.104
2009-03-13T14:57:00	Sturle Sunde	v21	50000	5000000						3	0.104
2009-07-20T19:19:00	Lupo	yorick	50000	5000000						3	0.104
2009-10-09T02:11:00	JimBa	FWserv			984829087269388376423	69.738		1		1	-
2016-12-30T15:08:45	TJAOI	Manual testing	50000	5000000						62	2.156
2016-12-30T15:08:45	TJAOI	Manual testing	50000	5000000	325041907948871839553	68.139	23	2		23	0.800
2017-04-07T16:06:15	TJAOI	Manual testing	50000	5000000						90	3.130
2017-12-01T13:34:26	TJAOI	Manual testing	50000	5000000						91	3.165
2020-01-06T12:23:19	TJAOI	Manual testing	250000	25000000						44	7.651

Lucas-Lehmer results:
No L-L results for M1002647

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T15:59:47

Oliver Kruse

GTX-0

325041907948871839553

984829087269388376423

B8AF8B0E81FA4F36

2017-10-05T21:00:54

Oliver Kruse

Manual testing

325041907948871839553

984829087269388376423

B8AF8B0E81FA4F__

2017-10-15T14:11:08

Oliver Kruse

Threadripper

325041907948871839553

984829087269388376423

B8AF8B0E81FA4F__

2017-12-25T05:09:05

ATH

ec2-1xf

325041907948871839553

984829087269388376423

B8AF8B0E81FA4F__

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 = 1110000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 600000, B2 = 800000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 400000, B2 = 600000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000, B2 = 400000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 98000 (P-1 stage 1)

B1 = 78000 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-11T22:45:03+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