M2176547 Mersenne number exponent details

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M2176547

<<<

>>>

is 2 ^2176547 - 1

has 655206 decimal digits

takes 0.143 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	0849F817E2D4AD4C	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	2⁶⁸	27.3851	67.6471%	5000000	200000000	1.4896	8.9481%	28.8746	70.5420%	2.8950%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8574%	0.0195	63.1528%	1.0839%
GPU72	2⁶²	0.2823	64.5161%	11000	160000	0.0018	1.5682%	0.2841	65.0726%	0.5565%
Difference	+6	+27.1028	+3.1309%	+4989000	+199840000	+1.4877	+7.3799%	+28.5905	+5.4694%	+5.4694%

Known prime factors (1 factor, 90.9 bits, 0.00417420% 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
2176547	2236683353680191741740340521	28	90.853	513814623272594559580 2² × 5 × 7 × 97 × 163 × 181 × 51131 × 25081657	2019-11-22	51131	25081657	122,184,413	0.1349	0.2433

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-05T01:17:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-08T01:30:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.354%
2011-01-15T01:41:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.204%
2014-06-13T02:40:00	Jocelyn Larouche	Manual testing	119489	119489		-		-	-	0.011	-	-	0.890%
2014-10-05T22:22:00	Jocelyn Larouche	Manual testing	148978	148978		-		-	-	0.014	-	-	1.007%
2015-12-22T14:03:57	HBendtz	Manual testing	700000	21000000	12	-		-	-	0.172	-	-	5.205%
2019-11-22T18:12:03	mikr	MSI	5000000	200000000	12		2236683353680191741740340521	28	90.853	1.490	0.286	2.979	8.948%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-05T05:04:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-07T22:32:00	Sturle Sunde	gonsha.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-09-09T08:39:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.451	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.902	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.717	-	-
2016-01-02T13:50:57	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.433	-	-
2016-11-17T17:00:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.867	-	-
2019-04-29T13:20:33	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.73	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.334 GHz-days
Estimated T-Level:	1.950

Digits	B1	Curves	Complete	FacMiss
20	11000	39 / 100	0.390	67.573%
25	50000	39 / 280	0.139	86.976%

New Calculation Method

Total ECM effort:	3.334 GHz-days
Estimated T-Level:	1.950

Digits	B1	Complete	FacMiss
20	11000	1.258	28.420%
25	50000	0.114	89.252%
30	250000	0.007	99.302%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.334

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-07T04:23:00	Helgen	newone	50000	5000000						3	0.256
2009-12-06T08:40:00	SubPrime	abd0	50000	5000000						3	0.256
2011-08-28T00:52:00	Bud	annan	50000	5000000						3	0.256
2013-05-13T14:19:00	Xyzzy	J	50000	5000000						3	0.256
2015-02-23T19:08:00	Jason U	Server7	50000	5000000						3	0.256
2015-11-07T21:19:14	dragon325	Falken-i7-920	50000	5000000						3	0.256
2016-03-05T09:53:17	Bruce	Desk6	50000	5000000						3	0.256
2016-06-23T05:08:43	Jason U	Server7	50000	5000000						3	0.256
2016-10-22T11:22:15	Bruce	Desk6	50000	5000000						3	0.256
2017-04-05T14:57:08	Bruce	Desk6	50000	5000000						3	0.256
2017-10-31T07:00:43	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2018-03-09T13:50:30	Bruce	Desk6	50000	5000000						3	0.256
2018-08-23T11:11:34	Bruce	Desk6	50000	5000000						3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	0849F817E2D4AD4C	0.143
2018-04-12T23:33:17	kkmrkkblmbrbk	old	0849F817E2D4AD4C	0.143

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-11-23T05:31:04

mnd9

eileen

2236683353680191741740340521

103DCB62BB9D93B3

2019-11-30T02:48:24

Nesowa

Laptop

2236683353680191741740340521

103DCB62BB9D93B3

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 700000, B2 = 21000000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148978 (P-1 stage 1)

B1 = 119489 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-11-30T02:48:24+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