M2181349 Mersenne number exponent details

is 2 ^2181349 - 1

has 656652 decimal digits

takes 0.143 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	2⁶⁸	27.3248	67.6471%	2500000	125000000	0.8746	7.9283%	28.1994	70.2121%	2.5650%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8586%	0.0194	63.1533%	1.0843%
GPU72	2⁶²	0.2816	64.5161%	11000	160000	0.0018	1.5689%	0.2835	65.0728%	0.5567%
Difference	+6	+27.0431	+3.1309%	+2489000	+124840000	+0.8728	+6.3594%	+27.9160	+5.1393%	+5.1393%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2181349	642119273632998561359	21	69.121	147183984230171 7 × 7937 × 2649147469	2020-03-11	7937	2649147469	89.030	13.761	25.700

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2011-01-14T04:06:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.204%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	119424	119424		-		-	-	0.011	-	-	0.890%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148848	148848		-		-	-	0.014	-	-	1.007%
2016-01-04T02:12:25	Jocelyn Larouche	Manual testing	443432	4434320	6	-		-	-	0.063	-	-	3.589%
2018-01-23T17:14:23	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.928%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-02T10:43:00	Sturle Sunde	krebs.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-06T14:54:00	Sturle Sunde	eberlin.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-09-13T20:29:00	BloodIce	Manual testing	2⁶²	2⁶³		-	-	0.450	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.900	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.713	-	-
2016-01-02T13:50:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.426	-	-
2016-11-24T19:46:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.851	-	-
2019-04-22T13:11:41	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.70	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.045 GHz-days
Estimated T-Level:	2.950

Digits	B1	Curves	Complete	FacMiss
20	11000	59 / 100	0.590	55.268%
25	50000	59 / 280	0.211	80.970%

New Calculation Method

Total ECM effort:	5.045 GHz-days
Estimated T-Level:	2.950

Digits	B1	Complete	FacMiss
20	11000	1.903	14.909%
25	50000	0.172	84.197%
30	250000	0.011	98.946%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	4.874
50000	5000000	642119273632998561359	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-24T22:00:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.257
2009-12-09T12:24:00	SubPrime	stor	50000	5000000						3	0.257
2011-08-30T17:17:00	Bud	annan	50000	5000000						3	0.257
2013-05-15T17:48:00	Xyzzy	J	50000	5000000						3	0.257
2015-02-27T06:17:00	Jason U	Server7	50000	5000000						3	0.257
2015-11-25T03:37:26	lopper	i5-4670	50000	5000000						3	0.257
2016-03-10T10:38:21	S36049	Wolle5	50000	5000000						3	0.257
2016-06-24T08:37:22	Bruce	Desk6	50000	5000000						3	0.257
2016-10-27T15:09:23	Bruce	Desk6	50000	5000000						3	0.257
2017-04-09T20:26:07	Bruce	Desk6	50000	5000000						3	0.257
2017-11-02T11:47:17	Bruce	Desk6	50000	5000000						3	0.257
2018-03-12T12:02:48	Bruce	Desk6	50000	5000000						3	0.257
2018-08-28T15:15:41	Bruce	Desk6	50000	5000000						3	0.257
2020-01-29T00:58:04	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.257
2020-02-05T07:20:01	mnd9	27016b	50000	5000000						3	0.257
2020-02-12T21:42:59	mnd9	f4b	50000	5000000						3	0.257
2020-02-21T15:02:46	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.257
2020-03-04T14:18:12	mnd9	office2	50000	5000000						3	0.257
2020-03-05T02:26:26	Sergey Nosov	TS140-02	50000	5000000						3	0.257
2020-03-11T13:39:25	mnd9	office2	50000	5000000	642119273632998561359	69.121	2	2	5194758439711766	2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	2E03139A6DB76C4E	0.143
2018-04-13T17:43:39	kkmrkkblmbrbk	old	2E03139A6DB76C4E	0.143

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-03-12T08:02:46

Jinyuan Wang

Manual testing

642119273632998561359

1EA04A1D77601C88

2020-03-13T07:29:14

Chang Chia-Tche

homura

642119273632998561359

1EA04A1D77601C88

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 443432, B2 = 4434320 (P-1 stage 2)

B1 = 443432 (P-1 stage 1)

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

B1 = 148848 (P-1 stage 1)

B1 = 119424 (P-1 stage 1)

B1 = 90000 (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

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-03-13T07:29:14+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