M5938781 Mersenne number exponent details

Residue

Status

L-L

98FDB22938CAE337

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	2⁶⁷	5.0034	65.6716%	360000	8910000	0.2122	5.0971%	5.2156	67.4214%	1.7498%
PrimeNet	2⁶²	0.1034	62.9032%	26000	600000	0.0147	3.3241%	0.1182	64.1364%	1.2331%
GPU72	2⁶⁶	2.4868	65.1515%	40000	800000	0.0209	2.3438%	2.5077	65.9683%	0.8168%
Difference	+1	+2.5166	+0.5201%	+320000	+8110000	+0.1913	+2.7533%	+2.7079	+1.4531%	+1.4531%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.0034

65.6716%

360000

8910000

0.2122

5.0971%

5.2156

67.4214%

1.7498%

PrimeNet

2⁶²

0.1034

62.9032%

26000

600000

0.0147

3.3241%

0.1182

64.1364%

1.2331%

GPU72

2⁶⁶

2.4868

65.1515%

40000

800000

0.0209

2.3438%

2.5077

65.9683%

0.8168%

Difference

+2.5166

+0.5201%

+320000

+8110000

+0.1913

+2.7533%

+2.7079

+1.4531%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5938781	1675378451786240267877964327	28	90.437	141054069158825714223 3 × 1193 × 51197 × 769802660321	2016-05-09	51197	769802660321	61,440,335	10,778	20,130

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5938781

1675378451786240267877964327

90.437

141054069158825714223
3 × 1193 × 51197 × 769802660321

2016-05-09

51197

769802660321

61,440,335

10,778

20,130

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-10-15T00:00:00	ANONYMOUS	v4_computers	20000	65000		-		-	-	0.006	-	-	0.758%
2011-03-17T19:53:00	harlee	P4_2600	70000	1120000		-		-	-	0.033	-	-	2.528%
2014-11-16T08:09:00	Nesowa	newfs	360000	8910000		-		-	-	0.212	-	-	5.097%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.052	-	-
1998-09-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.103	-	-
1998-09-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.103	-	-
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.103	-	-
2016-02-23T16:39:14	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.165	-	-
2014-09-29T09:32:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.331	-	-
2014-10-01T02:05:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.629	-	-
2015-09-20T21:47:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.258	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.078 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	1.078 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.129	87.895%
25	50000	0.012	98.841%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.808
50000	5000000	1675378451786240267877964327	1	0.269

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-08-20T01:37:00	JimBa	Dell	50000	5000000						3	0.808
2016-05-10T00:29:25	Bruce	desk	50000	5000000	1675378451786240267877964327	90.437	1	2		1	0.269

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	98FDB22938CAE337	1.052
2000-12-07T00:00:00	ANONYMOUS	v4_computers	98FDB22938CAE337	1.052
2015-05-02T00:00:00	MadPoo	Manual testing	98FDB22938CAE337	1.052

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T17:59:46

kkmrkkblmbrbk

Manual testing

1675378451786240267877964327

245330CBCEFDDE__

2018-09-13T03:32:25

ANONYMOUS

1675378451786240267877964327

245330CBCEFDDE__

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 = 360000, B2 = 8910000 (P-1 stage 2)

B1 = 360000 (P-1 stage 1)

B1 = 70000, B2 = 1120000 (P-1 stage 2)

B1 = 70000 (P-1 stage 1)

B1 = 20000, B2 = 65000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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