M1877857 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	15.8233	68.6567%	500000	15000000	0.1015	5.0844%	15.9248	70.2503%	1.5936%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0314%	0.0116	64.2747%	1.1168%
GPU72	2⁶¹	0.1636	65.5738%	10000	150000	0.0014	1.6911%	0.1650	66.1559%	0.5822%
Difference	+6	+15.6597	+3.0829%	+490000	+14850000	+0.1001	+3.3933%	+15.7598	+4.0944%	+4.0944%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.8233

68.6567%

500000

15000000

0.1015

5.0844%

15.9248

70.2503%

1.5936%

PrimeNet

2⁵⁷

0.0102

63.1579%

9000

160000

0.0014

3.0314%

0.0116

64.2747%

1.1168%

GPU72

2⁶¹

0.1636

65.5738%

10000

150000

0.0014

1.6911%

0.1650

66.1559%

0.5822%

Difference

+15.6597

+3.0829%

+490000

+14850000

+0.1001

+3.3933%

+15.7598

+4.0944%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1877857	8968645033	10	33.062	2388 2² × 3 × 199	-	4	199	9.244e-10	1.150e-6	1.597e-6
1877857	82956210833	11	36.272	22088 2³ × 11 × 251	2008-07-15	11	251	8.682e-9	1.894e-6	2.043e-6
1877857	2370945884146541132183	22	71.006	631290317672363 79 × 88853 × 89935249	2020-10-11	88853	89935249	282.32	0.3920	0.7199

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1877857

8968645033

33.062

2388
2² × 3 × 199

199

9.244e-10

1.150e-6

1.597e-6

1877857

82956210833

36.272

22088
2³ × 11 × 251

2008-07-15

251

8.682e-9

1.894e-6

2.043e-6

1877857

2370945884146541132183

71.006

631290317672363
79 × 88853 × 89935249

2020-10-11

88853

89935249

282.32

0.3920

0.7199

exponent	prime factors	composite factor	digits	bits*
1877857	8968645033 82956210833	744004808243886242489	21	69.334
1877857	8968645033 2370945884146541132183	21264172027362669569283259397039	32	104.068
1877857	82956210833 2370945884146541132183	196684686638894058429079469538439	33	107.278
1877857	8968645033 82956210833 2370945884146541132183	1763995137891078661743175367238195739923487	43	140.340

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:39:01	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 8968645033 skipped known factor: 82956210833	-	-	0.101	-	-	5.084%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:39:01

alpertron

Manual testing

500000

15000000

skipped known factor: 8968645033
skipped known factor: 82956210833

0.101

-

-

5.084%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	82956210833	36.272	11	3.80720e-9	0.217	8.12414e-9

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:47:00

J Feitsma

Manual testing

82956210833

36.272

3.80720e-9

0.217

8.12414e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.910 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	19.910 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.801	0.015%
25	50000	0.797	45.060%
30	250000	0.049	95.189%
35	1000000	0.002	99.774%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		3	0.126
50000	5000000		31	2.147
50000	5000000	2370945884146541132183	3	0.208
50000	6600000		216	16.88
50000	6750000		7	0.553

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-04-08T14:33:09	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-19T15:40:21	alpertron		50000	5000000						3	0.208
2018-09-28T16:57:58	alpertron	Manual testing	50000	5000000						3	0.208
2020-08-04T03:37:37	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.208
2020-10-11T05:24:12	nordi	sweet16	50000	5000000	2370945884146541132183	71.006	3	2	2556881850846160	3	0.208
2020-10-31T18:15:01	Ahmed Azhad	c5.large.az	50000	5000000						7	0.485
2021-01-22T10:47:46	nordi	sweet16	50000	6750000						7	0.553
2021-05-12T01:27:18	Chang Chia-Tche	exbpc13	50000	5000000						7	0.485
2021-08-14T16:48:37	ArtyomP	axioo	50000	50000						3	0.126
2021-08-25T22:28:15	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.485
2021-09-29T12:10:54	TJAOI	Manual testing	50000	6600000						216	16.88

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T13:03:56

Oliver Kruse

GTX-2

8968645033

82956210833

3BA075740DDF1E__

2017-11-08T01:15:57

ATH

ec2-1xf

8968645033

82956210833

3BA075740DDF1E__

2020-10-11T07:26:26

M Miller

cruncher

8968645033

82956210833

2370945884146541132183

D84DEB4D137718FF

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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