M2028227 Mersenne number exponent details

is 2 ^2028227 - 1

has 610558 decimal digits

takes 0.133 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	29.3877	69.1176%	4000000	200000000	1.3994	8.7520%	30.7871	71.8205%	2.7028%
PrimeNet	2⁵⁸	0.0189	63.7931%	9000	150000	0.0016	2.6140%	0.0205	64.7395%	0.9464%
GPU72	2⁶²	0.3029	66.1290%	8000	120000	0.0013	1.2744%	0.3042	66.5607%	0.4317%
Difference	+6	+29.0848	+2.9886%	+3992000	+199880000	+1.3981	+7.4776%	+30.4828	+5.2598%	+5.2598%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2028227	45252780945336744080679319	26	85.226	11155748578767747417 3 × 433 × 8587951176880483	2020-02-25	433	8587951176880483	5,667,072	44,607,965	83,315,257

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.221%
2007-11-17T00:00:00	markr	v4_computers	200000	3500000		-		-	-	0.036	-	-	3.026%
2010-12-14T09:47:00	Jocelyn Larouche	Manual testing	202822	202822		-		-	-	0.019	-	-	1.173%
2013-10-19T08:50:00	David Campeau	i5-2500k	580000	15080000		-		-	-	0.131	-	-	4.747%
2019-04-11T05:59:44	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.752%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-03T08:37:00	Sturle Sunde	gehry.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-02-07T06:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.151	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.484	-	-
2015-04-13T20:08:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.968	-	-
2015-04-13T20:08:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.842	-	-
2015-10-31T16:44:09	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.684	-	-
2016-07-06T22:01:14	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.369	-	-
2019-03-20T02:02:07	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.74	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.270 GHz-days
Estimated T-Level:	3.700

Digits	B1	Curves	Complete	FacMiss
20	11000	74 / 100	0.740	47.534%
25	50000	74 / 280	0.264	76.739%

New Calculation Method

Total ECM effort:	6.270 GHz-days
Estimated T-Level:	3.700

Digits	B1	Complete	FacMiss
20	11000	2.387	9.190%
25	50000	0.216	80.594%
30	250000	0.013	98.680%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		72	6.100
50000	5000000	45252780945336744080679319	2	0.169

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-05T02:14:00	Helgen	newone	50000	5000000						3	0.254
2009-11-13T12:15:00	SubPrime	mysql0	50000	5000000						3	0.254
2011-02-19T07:12:00	James Hintz	ryan	50000	5000000						3	0.254
2013-02-18T21:29:00	S00030	op9020-usff	50000	5000000						3	0.254
2014-03-22T07:24:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-04T18:11:00	guru	w6	50000	5000000						3	0.254
2015-11-26T07:47:29	mikr	MSI	50000	5000000						12	1.017
2017-05-14T23:43:14	Bruce	Desk6	50000	5000000						3	0.254
2017-11-14T14:47:29	Sebastian Hornbostel	V2	50000	5000000						3	0.254
2018-03-20T18:00:10	Bruce	Desk6	50000	5000000						3	0.254
2018-08-24T12:53:45	Bruce	Desk6	50000	5000000						3	0.254
2019-12-19T15:34:42	Brett Walker	brain	50000	5000000						3	0.254
2019-12-25T18:31:06	daveward2005	Davy	50000	5000000						3	0.254
2019-12-30T16:18:55	TheJudger	myECM	50000	5000000						3	0.254
2020-01-04T18:38:51	TheJudger	myECM	50000	5000000						3	0.254
2020-01-19T20:41:07	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-01-21T05:33:33	Keysarecool	Boat_Anchor	50000	5000000						3	0.254
2020-01-25T10:02:40	David_McCann	i5	50000	5000000						3	0.254
2020-02-02T18:10:10	daveward2005	MW	50000	5000000						3	0.254
2020-02-11T18:41:20	mnd9	75201b	50000	5000000						3	0.254
2020-02-18T02:56:28	mnd9	50869b	50000	5000000						3	0.254
2020-02-25T17:30:15	mnd9	libproj	50000	5000000	45252780945336744080679319	85.226	2	2	859248965020263	2	0.169

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	76A5D391BAB49B9B	0.133
2016-07-15T15:20:48	Mark Rose	donatello	76A5D391BAB49B9B	0.133

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-02-26T07:51:58

Christoph Zenger

Manual testing

45252780945336744080679319

F0BF97E55C631541

2020-02-27T00:08:16

Jinyuan Wang

Manual testing

45252780945336744080679319

F0BF97E55C631541

2020-02-28T16:50:15

Chang Chia-Tche

exbbbe-lt

45252780945336744080679319

F0BF97E55C631541

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 580000, B2 = 15080000 (P-1 stage 2)

B1 = 580000 (P-1 stage 1)

B1 = 200000, B2 = 3500000 (P-1 stage 2)

B1 = 202822 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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10¹⁶

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-02-28T16:50:15+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