M1378831 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	21.5501	68.6567%	3106900	111849000	0.5000	8.2190%	22.0501	71.2328%	2.5761%
PrimeNet	2⁵⁶	0.0070	62.5000%	6500	110000	0.0007	2.7540%	0.0076	63.5327%	1.0327%
GPU72	2⁶⁰	0.1114	65.0000%	5500	65000	0.0005	1.1706%	0.1119	65.4097%	0.4097%
Difference	+7	+21.4387	+3.6567%	+3101400	+111784000	+0.4995	+7.0484%	+21.9382	+5.8231%	+5.8231%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1378831	2953163190589209653007089	25	81.289	1070893818963023624 2³ × 23 × 59 × 1289 × 2791 × 27419771	2014-09-15	2791	27419771	487,719	0.0829	0.1545
1378831	544477335781983340278703289	27	88.815	197441650130430538724 2² × 17 × 311 × 331 × 611951 × 46091923	2014-09-15	611951	46091923	51,209,912	0.1711	0.2597

exponent	prime factors	composite factor	digits	bits*
1378831	2953163190589209653007089 544477335781983340278703289	16079304261414343677906375814174860781008844446157 21	52	170.104

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	15000	228750		-		-	-	0.001	-	-	0.814%
2014-04-15T00:10:00	ANONYMOUS	Manual testing	110000	110000		-		-	-	0.006	-	-	0.898%
2014-04-16T21:18:00	Jocelyn Larouche	Manual testing	120000	120000		-		-	-	0.007	-	-	0.944%
2014-04-22T10:35:00	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.011	-	-	1.243%
2014-09-15T15:11:00	mikr	MSI	3106900	111849000	12		2953163190589209653007089 544477335781983340278703289	52	170.104	0.500	0.105	1.000	8.219%
2016-03-17T19:05:33	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.898%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-07-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.028	-	-
2022-03-07T17:32:39	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.084	-	-
2009-02-24T01:31:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.111	-	-
2012-09-26T19:26:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.223	-	-
2013-01-23T08:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.712	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.297 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.297 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.78
250000	35000000		50	13.52

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-29T02:46:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-11-30T12:32:00	S36049	Wolle3	50000	5000000						3	0.141
2009-05-13T13:17:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.141
2009-08-11T20:11:00	greensinoz	giopa01	50000	5000000						3	0.141
2009-12-10T11:47:00	Lupo	yorick	50000	5000000						3	0.141
2010-12-18T15:04:00	Lackó	Iroda_Eva	50000	5000000						3	0.141
2011-04-12T17:29:00	James Hintz	chris3	50000	5000000						3	0.141
2012-03-11T08:36:00	Scott Kurowski	DM6400	50000	5000000						3	0.141
2012-10-26T00:20:00	OS1	Tina	50000	5000000						3	0.141
2013-09-07T02:34:00	jim f in mn	asus	50000	5000000						3	0.141
2014-03-01T02:53:00	Bruce	snowflake	50000	5000000						3	0.141
2014-03-15T03:44:00	Bruce	snowflake	50000	5000000						3	0.141
2018-12-07T13:08:02	TJAOI	Manual testing	50000	5000000						217	10.18
2021-12-10T12:32:52	TJAOI	Manual testing	250000	35000000						50	13.52

date	userid	compid	res64	spent (GHz-days)
2002-10-07T00:00:00	ANONYMOUS	v4_computers	665689B02747EC5A	0.053

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T11:48:59

Oliver Kruse

GTX-1

2953163190589209653007089

544477335781983340278703289

B42131F578B2CFF2

2017-10-05T21:17:20

Oliver Kruse

Manual testing

2953163190589209653007089

544477335781983340278703289

B42131F578B2CF__

2017-10-24T15:57:10

kkmrkkblmbrbk

old

2953163190589209653007089

544477335781983340278703289

B42131F578B2CF__

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 = 3106900, B2 = 111849000 (P-1 stage 2)

B1 = 3106900 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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