M1882247 Mersenne number exponent details

Residue

Status

L-L

5EF7AA0665E5E25F

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	15.7864	68.6567%	500000	15000000	0.1015	5.0858%	15.8879	70.2508%	1.5941%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0328%	0.0116	64.2752%	1.1173%
GPU72	2⁶¹	0.1632	65.5738%	10000	150000	0.0014	1.6918%	0.1646	66.1562%	0.5824%
Difference	+6	+15.6232	+3.0829%	+490000	+14850000	+0.1001	+3.3940%	+15.7233	+4.0946%	+4.0946%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.7864

68.6567%

500000

15000000

0.1015

5.0858%

15.8879

70.2508%

1.5941%

PrimeNet

2⁵⁷

0.0102

63.1579%

9000

160000

0.0014

3.0328%

0.0116

64.2752%

1.1173%

GPU72

2⁶¹

0.1632

65.5738%

10000

150000

0.0014

1.6918%

0.1646

66.1562%

0.5824%

Difference

+15.6232

+3.0829%

+490000

+14850000

+0.1001

+3.3940%

+15.7233

+4.0946%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1882247	1783813393074621411362729	25	80.561	473852101524035212 2² × 11² × 31 × 809 × 39037970717	2009-12-23	809	39037970717	177,174	167.31	312.48

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1882247

1783813393074621411362729

80.561

473852101524035212
2² × 11² × 31 × 809 × 39037970717

2009-12-23

809

39037970717

177,174

167.31

312.48

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:39:37	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.086%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:39:37

alpertron

Manual testing

500000

15000000

0.101

-

-

5.086%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-01-09T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.020

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.625 GHz-days
Estimated T-Level:	24.554

Digits	B1	Curves	Complete	FacMiss
20	11000	255 / 100	2.550	7.709%
25	50000	255 / 280	0.911	40.158%

New Calculation Method

Total ECM effort:	19.625 GHz-days
Estimated T-Level:	24.554

Digits	B1	Complete	FacMiss
20	11000	10.513	0.003%
25	50000	0.968	38.001%
30	250000	0.061	94.044%
35	1000000	0.003	99.712%

ECM Summary

B1	B2	factor	curves	GHz-days
		1783813393074621411362729	1	0.00000e+0
50000	5000000		35	2.425
50000	6600000		213	16.65
50000	6750000		7	0.553

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-20T08:36:00	Rob_Dee	twopc	50000	5000000						1	0.069
2009-07-21T20:05:00	James Hintz	06_071509	50000	5000000						3	0.208
2009-12-23T05:22:00	Dmitry B. Khachaturov	mgp1-1			1783813393074621411362729	80.561		1		1	-
2020-08-15T20:14:11	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.208
2020-10-18T22:12:31	Chang Chia-Tche	exbpc13	50000	5000000						7	0.485
2021-01-07T03:14:50	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.485
2021-04-03T16:40:42	Chang Chia-Tche	exbpc13	50000	5000000						7	0.485
2021-07-15T15:41:58	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-09-29T16:44:34	Dylan Delgado	colab	50000	6750000						7	0.553
2021-10-28T13:39:17	TJAOI	Manual testing	50000	6600000						213	16.65

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	Ethan O'Connor	v4_computers	5EF7AA0665E5E25F	0.102

date

userid

compid

res64

spent (GHz-days)

1999-01-02T00:00:00

Ethan O'Connor

v4_computers

5EF7AA0665E5E25F

0.102

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 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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