M3737197 Mersenne number exponent details

Residue

Status

L-L

D187EC8BB0046CD9

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	7.9509	67.1642%	500000	130364850	1.1537	7.7700%	9.1045	69.7155%	2.5513%
PrimeNet	2⁶⁰	0.0411	63.3333%	16000	320000	0.0050	3.0890%	0.0461	64.4660%	1.1326%
GPU72	2⁶⁴	0.9524	65.6250%	22000	450000	0.0069	2.1094%	0.9593	66.3501%	0.7251%
Difference	+3	+6.9985	+1.5392%	+478000	+129914850	+1.1468	+5.6606%	+8.1452	+3.3654%	+3.3654%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.9509

67.1642%

500000

130364850

1.1537

7.7700%

9.1045

69.7155%

2.5513%

PrimeNet

2⁶⁰

0.0411

63.3333%

16000

320000

0.0050

3.0890%

0.0461

64.4660%

1.1326%

GPU72

2⁶⁴

0.9524

65.6250%

22000

450000

0.0069

2.1094%

0.9593

66.3501%

0.7251%

Difference

+6.9985

+1.5392%

+478000

+129914850

+1.1468

+5.6606%

+8.1452

+3.3654%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3737197	4340568921571938817608763001	28	91.810	580725196125858339500 2² × 5³ × 7⁴ × 227 × 43261 × 49259057	2015-10-23	43261	49259057	150,453,238	0.4149	0.7634

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3737197

4340568921571938817608763001

91.810

580725196125858339500
2² × 5³ × 7⁴ × 227 × 43261 × 49259057

2015-10-23

43261

49259057

150,453,238

0.4149

0.7634

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T11:19:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	1.149%
2013-02-09T04:25:00	Squeeky_Squirrel	T7500_2200	85000	1445000		-		-	-	0.024	-	-	2.600%
2015-10-23T02:09:07	mikr	MSI	1600000	66000000	12		4340568921571938817608763001	28	91.810	0.778	0.785	1.556	7.946%
2022-05-17T01:12:25	Jocelyn Larouche	Manual testing	500000	130364850		-	skipped known factor: 4340568921571938817608763001	-	-	1.154	-	-	7.770%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-06T05:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-05-08T16:13:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.082	-	-
2012-05-10T01:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.427	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.525	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.000	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.344 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.344 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.344

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-02T19:27:00	oodaira	Linux01	50000	5000000						3	0.448
2012-06-02T22:55:00	LaurV	bc1	50000	5000000						3	0.448
2012-06-05T02:45:00	LaurV	Manual testing	50000	5000000						3	0.448

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-23T00:00:00	ANONYMOUS	v4_computers	D187EC8BB0046CD9	0.393
1999-10-29T00:00:00	ANONYMOUS	v4_computers	D187EC8BB0046CD9	0.393

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:17:34

kkmrkkblmbrbk

Manual testing

4340568921571938817608763001

B527209CC217EF__

2017-12-03T09:13:29

Oliver Kruse

GTX-0

4340568921571938817608763001

B527209CC217EF__

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 = 500000, B2 = 130364850 (P-1 stage 2)

B1 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 85000, B2 = 1445000 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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