M1625993 Mersenne number exponent details

Residue

Status

L-L

8FA0E6B7D10CA9B7

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	18.2743	68.6567%	1000000	20000000	0.1318	5.6783%	18.4061	70.4365%	1.7798%
PrimeNet	2⁵⁷	0.0118	63.1579%	7000	120000	0.0009	2.5561%	0.0127	64.0996%	0.9417%
GPU72	2⁶¹	0.1889	65.5738%	6500	65000	0.0006	1.0899%	0.1895	65.9490%	0.3752%
Difference	+6	+18.0854	+3.0829%	+993500	+19935000	+0.1312	+4.5884%	+18.2166	+4.4875%	+4.4875%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.2743

68.6567%

1000000

20000000

0.1318

5.6783%

18.4061

70.4365%

1.7798%

PrimeNet

2⁵⁷

0.0118

63.1579%

7000

120000

0.0009

2.5561%

0.0127

64.0996%

0.9417%

GPU72

2⁶¹

0.1889

65.5738%

6500

65000

0.0006

1.0899%

0.1895

65.9490%

0.3752%

Difference

+18.0854

+3.0829%

+993500

+19935000

+0.1312

+4.5884%

+18.2166

+4.4875%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1625993	429257111231910129617081	24	78.506	131998449941638780 2² × 5 × 17 × 19 × 47 × 434748863519	2019-11-04	47	434748863519	66,822	1,534.1	2,865.2
1625993	6969786019200890681365337	25	82.527	2143239859950470476 2² × 13 × 107 × 179 × 2293 × 938483347	2013-11-11	2293	938483347	1,159,909	3.3117	6.1851

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1625993

429257111231910129617081

78.506

131998449941638780
2² × 5 × 17 × 19 × 47 × 434748863519

2019-11-04

434748863519

66,822

1,534.1

2,865.2

1625993

6969786019200890681365337

82.527

2143239859950470476
2² × 13 × 107 × 179 × 2293 × 938483347

2013-11-11

2293

938483347

1,159,909

3.3117

6.1851

exponent	prime factors	composite factor	digits	bits*
1625993	429257111231910129617081 6969786019200890681365337	2991830212506728841625903657506245022346076521297	49	161.034

exponent

prime factors

composite factor

digits

bits*

1625993

429257111231910129617081
6969786019200890681365337

2991830212506728841625903657506245022346076521297

161.034

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-12-06T18:05:00	BigBrother	Winston	1000000	20000000		-		-	-	0.132	-	-	5.678%
2016-03-17T19:17:33	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	4.997%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2010-04-30T08:20:00	Architects Cubed	a3_lm	2⁶⁰	2⁶¹		-	-	0.094	-	-
2010-08-22T04:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.982	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.927 GHz-days
Estimated T-Level:	24.429

Digits	B1	Curves	Complete	FacMiss
20	11000	248 / 100	2.480	8.270%
25	50000	248 / 280	0.886	41.177%

New Calculation Method

Total ECM effort:	13.927 GHz-days
Estimated T-Level:	24.429

Digits	B1	Complete	FacMiss
20	11000	8.000	0.034%
25	50000	0.723	48.528%
30	250000	0.045	95.645%
35	1000000	0.002	99.796%

ECM Summary

B1	B2	factor	curves	GHz-days
		6969786019200890681365337	1	0.00000e+0
50000	5000000		205	11.51
50000	5000000	429257111231910129617081	43	2.415

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-04-29T08:06:00	James Heinrich	Q6600	50000	5000000						3	0.168
2009-05-30T20:37:00	Lupo	yorick	50000	5000000						3	0.168
2010-04-20T19:09:00	James Classen	towerofart	50000	5000000						3	0.168
2011-09-05T08:26:00	S36049	Wolle5	50000	5000000						3	0.168
2013-02-27T16:59:00	Donna Noble	opt4820	50000	5000000						3	0.168
2013-11-11T05:06:00	Chang Chia-Tche	exbpc13			6969786019200890681365337	82.527		1		1	-
2019-11-04T17:13:49	TJAOI	Manual testing	50000	5000000	429257111231910129617081	78.506	43	2		43	2.415
2019-11-11T13:14:23	TJAOI	Manual testing	50000	5000000						190	10.67

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	8FA0E6B7D10CA9B7	0.073

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

8FA0E6B7D10CA9B7

0.073

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T15:03:16

Oliver Kruse

GTX-2

6969786019200890681365337

FFD94F012E6EFF__

2017-11-01T16:52:45

kkmrkkblmbrbk

c4.xlarge

6969786019200890681365337

FFD94F012E6EFF__

2019-11-04T18:40:49

mnd9

printer

429257111231910129617081

6969786019200890681365337

0B00F5B275532620

2019-11-04T18:54:24

ATH

ec2-PRPCFDC

429257111231910129617081

6969786019200890681365337

0B00F5B275532620

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 = 1000000, B2 = 20000000 (P-1 stage 2)

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

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

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