M1955609 Mersenne number exponent details

Residue

Status

L-L

CD8E670D1EC7E087

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	15.1942	68.6567%	1000000	30000000	0.2029	6.2379%	15.3972	70.6119%	1.9552%
PrimeNet	2⁵⁸	0.0196	63.7931%	8000	140000	0.0012	2.4681%	0.0208	64.6867%	0.8936%
GPU72	2⁶²	0.3142	66.1290%	8000	90000	0.0010	1.1538%	0.3151	66.5198%	0.3908%
Difference	+5	+14.8800	+2.5277%	+992000	+29910000	+0.2020	+5.0841%	+15.0820	+4.0920%	+4.0920%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.1942

68.6567%

1000000

30000000

0.2029

6.2379%

15.3972

70.6119%

1.9552%

PrimeNet

2⁵⁸

0.0196

63.7931%

8000

140000

0.0012

2.4681%

0.0208

64.6867%

0.8936%

GPU72

2⁶²

0.3142

66.1290%

8000

90000

0.0010

1.1538%

0.3151

66.5198%

0.3908%

Difference

+14.8800

+2.5277%

+992000

+29910000

+0.2020

+5.0841%

+15.0820

+4.0920%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1955609	85718316241670049983	20	66.216	21916015993399 11² × 181124099119	2012-11-26	121	181124099119	11.355	776.25	1,449.8
1955609	21362302500265721163977	23	74.177	5461803075222532 2² × 59 × 23143233369587	2021-02-28	59	23143233369587	2,689.8	99,186	185,252

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1955609

85718316241670049983

66.216

21916015993399
11² × 181124099119

2012-11-26

121

181124099119

11.355

776.25

1,449.8

1955609

21362302500265721163977

74.177

5461803075222532
2² × 59 × 23143233369587

2021-02-28

23143233369587

2,689.8

99,186

185,252

exponent	prime factors	composite factor	digits	bits*
1955609	85718316241670049983 21362302500265721163977	1831140601367995883692851007211862529062391	43	140.394

exponent

prime factors

composite factor

digits

bits*

1955609

85718316241670049983
21362302500265721163977

1831140601367995883692851007211862529062391

140.394

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-05-10T09:03:00	kurly	hex	1000000	30000000		-		-	-	0.203	-	-	6.238%
2016-03-17T19:19:17	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.109%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2010-01-14T20:52:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.079	-	-
2011-08-27T22:19:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.816	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.368 GHz-days
Estimated T-Level:	24.411

Digits	B1	Curves	Complete	FacMiss
20	11000	247 / 100	2.470	8.354%
25	50000	247 / 280	0.882	41.324%

New Calculation Method

Total ECM effort:	20.368 GHz-days
Estimated T-Level:	24.411

Digits	B1	Complete	FacMiss
20	11000	10.247	0.004%
25	50000	0.969	37.964%
30	250000	0.062	94.008%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
		85718316241670049983	1	0.00000e+0
50000	5000000		9	0.626
50000	5000000	21362302500265721163977	5	0.348
50000	6750000		14	1.112
50000	6753682		7	0.556
50000	7500000		212	17.73

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-16T17:44:00	Candide	CA7E13832	50000	5000000						3	0.209
2009-08-17T05:45:00	SubPrime	stor	50000	5000000						3	0.209
2011-01-17T12:53:00	Lupo	yorick	50000	5000000						3	0.209
2012-11-26T01:51:00	Donna Noble	i3-2100t			85718316241670049983	66.216		1		1	-
2021-02-28T17:55:49	Poao	justg-ZA	50000	5000000	21362302500265721163977	74.177	5	2	8980873228998009	5	0.348
2021-05-19T08:12:05	Dylan Delgado	laptop-i78750	50000	6750000						7	0.556
2021-08-28T00:48:08	Dylan Delgado	colab	50000	6750000						7	0.556
2021-12-17T17:05:47	ZacHFX	5950X	50000	6753682						7	0.556
2022-05-12T09:18:33	TJAOI	Manual testing	50000	7500000						212	17.73

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	CD8E670D1EC7E087	0.106

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

CD8E670D1EC7E087

0.106

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T06:49:05

Oliver Kruse

GTX-1

85718316241670049983

C7E3752B229776__

2017-11-11T16:49:16

kkmrkkblmbrbk

c4.xlarge

85718316241670049983

C7E3752B229776__

2021-03-02T15:32:03

-Anonymous-

85718316241670049983

21362302500265721163977

6CB31631783C21__

2021-03-15T13:10:04

Anton Repko

DeskMini

85718316241670049983

21362302500265721163977

6CB31631783C2164

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 = 30000000 (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

10¹³

10¹⁴

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