M1195189 Mersenne number exponent details

Residue

Status

L-L

E95ADEFD05EB790D

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	24.8613	68.6567%	300000	10000000	0.0368	4.1591%	24.8981	69.9603%	1.3036%
PrimeNet	2⁵⁶	0.0080	62.5000%	5000	80000	0.0004	2.2681%	0.0084	63.3506%	0.8506%
GPU72	2⁶⁰	0.1285	65.0000%	5000	28000	0.0003	0.8021%	0.1288	65.2808%	0.2808%
Difference	+7	+24.7328	+3.6567%	+295000	+9972000	+0.0366	+3.3569%	+24.7693	+4.6796%	+4.6796%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

24.8613

68.6567%

300000

10000000

0.0368

4.1591%

24.8981

69.9603%

1.3036%

PrimeNet

2⁵⁶

0.0080

62.5000%

5000

80000

0.0004

2.2681%

0.0084

63.3506%

0.8506%

GPU72

2⁶⁰

0.1285

65.0000%

5000

28000

0.0003

0.8021%

0.1288

65.2808%

0.2808%

Difference

+24.7328

+3.6567%

+295000

+9972000

+0.0366

+3.3569%

+24.7693

+4.6796%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1195189	2456387529572792561	19	61.091	1027614682520 2³ × 5 × 23 × 1116972481	2007-10-21	23	1116972481	0.3750	2.7061	5.0542

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1195189

2456387529572792561

61.091

1027614682520
2³ × 5 × 23 × 1116972481

2007-10-21

1116972481

0.3750

2.7061

5.0542

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-05-11T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.44667e-5	-	-	0.005%
2002-09-22T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.049%
2002-09-22T00:00:00	Jocelyn Larouche	v4_computers	5000	5000		-		-	-	0.000	-	-	0.065%
2002-09-29T00:00:00	Jocelyn Larouche	v4_computers	8000	8000		-		-	-	0.000	-	-	0.111%
2002-10-07T00:00:00	Jocelyn Larouche	v4_computers	10000	10000		-		-	-	0.000	-	-	0.140%
2003-09-21T00:00:00	ANONYMOUS	v4_computers	10000	1000000		-		-	-	0.003	-	-	0.991%
unknown			300000	10000000		-		-	-	0.037	-	-	4.159%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.008	-	-
2001-10-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.016	-	-
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.032	-	-
2022-04-12T21:45:13	LordJulius	Manual testing	2¹	2⁶¹		-	-	0.257	-	-
2022-04-12T21:45:13	LordJulius	Manual testing	2⁶¹	2⁶²	2456387529572792561	61.091	19	0.118	0.074	0.240
2022-04-12T21:45:13	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.821	-	-
2022-04-12T21:45:13	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	1.643	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.463 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	18.463 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		2456387529572792561	1	0.00000e+0
50000	5000000		281	10.36
250000	25000000		44	8.108

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-21T18:31:00	James Heinrich	WHS			2456387529572792561	61.091		1		1	-
2017-10-18T13:05:14	Oliver Kruse	ECM-HTC	50000	5000000						3	0.111
2017-11-10T15:32:12	TJAOI	Manual testing	50000	5000000						140	5.159
2018-07-27T12:42:13	TJAOI	Manual testing	50000	5000000						138	5.086
2020-08-28T11:14:17	TJAOI	Manual testing	250000	25000000						44	8.108

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T11:36:20

csaba

office

2456387529572792561

E7960D24A205E0__

2017-10-17T20:22:03

Oliver Kruse

GTX-1

2456387529572792561

E7960D24A205E0__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 10000, B2 = 1000000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 8000 (P-1 stage 1)

B1 = 5000 (P-1 stage 1)

B1 = 4000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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