M5018863 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

A74E9CDF6BE01C42

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁶	3,049.2950	69.7368%	3600000	120000000	1.9982	4.5383%	3,051.2932	71.1103%	1.3734%
PrimeNet	2⁶¹	0.0612	62.2951%	22000	450000	0.0091	3.3153%	0.0703	63.5451%	1.2500%
GPU72	2⁶⁵	1.4537	64.6154%	34000	700000	0.0141	2.4175%	1.4678	65.4708%	0.8554%
Difference	+11	+3,047.8414	+5.1215%	+3566000	+119300000	+1.9840	+2.1208%	+3,049.8254	+5.6395%	+5.6395%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁶

3,049.2950

69.7368%

3600000

120000000

1.9982

4.5383%

3,051.2932

71.1103%

1.3734%

PrimeNet

2⁶¹

0.0612

62.2951%

22000

450000

0.0091

3.3153%

0.0703

63.5451%

1.2500%

GPU72

2⁶⁵

1.4537

64.6154%

34000

700000

0.0141

2.4175%

1.4678

65.4708%

0.8554%

Difference

+11

+3,047.8414

+5.1215%

+3566000

+119300000

+1.9840

+2.1208%

+3,049.8254

+5.6395%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5018863	5786082744723500245538354639	28	92.225	576433620993788856713 576433620993788856713	2021-10-16	1	576433620993788856713	264,421,535	6.312e+12	1.179e+13

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5018863

5786082744723500245538354639

92.225

576433620993788856713
576433620993788856713

2021-10-16

576433620993788856713

264,421,535

6.312e+12

1.179e+13

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-09-15T00:00:00	ANONYMOUS	v4_computers	20000	20000		-		-	-	0.004	-	-	0.073%
2001-02-04T00:00:00	ANONYMOUS	v4_computers	20000	145000		-		-	-	0.005	-	-	0.240%
2009-08-07T16:10:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	0.663%
2012-10-10T14:00:00	James Heinrich	i7-920	65000	1235000		-		-	-	0.026	-	-	0.765%
2013-05-12T09:58:00	Squeeky_Squirrel	P4_2600	160000	3440000		-		-	-	0.068	-	-	1.299%
2018-08-29T17:15:06	mikr	MSI	3600000	120000000	12	-		-	-	1.998	-	-	4.538%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-10-16T22:28:01	ATH	5960X	2500000	85000000	2	7	5786082744723500245538354639	P+1	28	92.225	1.649

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-10-16T22:28:01

ATH

5960X

2500000

85000000

5786082744723500245538354639

P+1

92.225

1.649

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:07	Mark Rose	Manual testing	2¹	2⁶³		-	-	0.318	-	-
2012-06-27T11:26:00	dbaugh	Manual testing	2⁶³	2⁶⁴		-	-	0.391	-	-
2012-07-07T12:36:00	dbaugh	Manual testing	2⁶⁴	2⁶⁵		-	-	0.744	-	-
2012-07-14T05:29:00	dbaugh	Manual testing	2⁶⁵	2⁶⁶		-	-	1.489	-	-
2012-07-20T06:41:00	dbaugh	Manual testing	2⁶⁶	2⁶⁷		-	-	2.978	-	-
2012-08-06T09:49:00	ANONYMOUS	Manual testing	2⁶⁷	2⁶⁸		-	-	5.956	-	-
2012-08-12T07:07:00	dbaugh	Manual testing	2⁶⁸	2⁶⁹		-	-	11.91	-	-
2012-09-21T07:59:00	dbaugh	Manual testing	2⁶⁹	2⁷⁰		-	-	23.82	-	-
2012-11-19T10:35:00	dbaugh	Manual testing	2⁷⁰	2⁷¹		-	-	47.65	-	-
2013-02-23T08:46:00	dbaugh	Manual testing	2⁷¹	2⁷²		-	-	95.29	-	-
2013-04-30T08:16:00	dbaugh	Manual testing	2⁷²	2⁷³		-	-	190.6	-	-
2013-09-09T04:52:00	dbaugh	Manual testing	2⁷³	2⁷⁴		-	-	381.2	-	-
2013-10-08T08:40:00	dbaugh	Manual testing	2⁷⁴	2⁷⁵		-	-	762.3	-	-
2014-07-06T06:24:00	dbaugh	Manual testing	2⁷⁵	2⁷⁶		-	-	1,525	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.740 GHz-days
Estimated T-Level:	0.650

Digits	B1	Curves	Complete	FacMiss
20	11000	13 / 100	0.130	87.752%
25	50000	13 / 280	0.046	95.455%

New Calculation Method

Total ECM effort:	2.740 GHz-days
Estimated T-Level:	0.650

Digits	B1	Complete	FacMiss
20	11000	0.419	65.747%
25	50000	0.038	96.281%
30	250000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	2.740

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-06-29T14:45:00	Aca Arsov	backo6400	50000	5000000						3	0.632
2012-08-30T09:38:00	dbaugh	Manual testing	50000	5000000						10	2.108

date	userid	compid	res64	spent (GHz-days)
2001-03-05T00:00:00	ANONYMOUS	v4_computers	896C6C4E890EFB__	0.696

date

userid

compid

res64

spent (GHz-days)

2001-03-05T00:00:00

ANONYMOUS

v4_computers

896C6C4E890EFB__

0.696

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 = 3600000, B2 = 120000000 (P-1 stage 2)

B1 = 2500000, B2 = 85000000 (P+1 stage 2)

B1 = 3600000 (P-1 stage 1)

B1 = 2500000 (P+1 stage 1)

B1 = 160000, B2 = 3440000 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 65000, B2 = 1235000 (P-1 stage 2)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 20000, B2 = 145000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

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10²¹

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