M1965851 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	15.1150	68.6567%	-	-	-	-	15.1150	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0012	2.4706%	0.0207	64.6876%	0.8945%
GPU72	2⁶²	0.3125	66.1290%	8000	100000	0.0010	1.1954%	0.3135	66.5339%	0.4049%
Difference	+5	+14.8025	+2.5277%	-8000	-100000	-0.0010	-1.1954%	+14.8015	+2.1228%	+2.1228%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.1150

68.6567%

15.1150

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0012

2.4706%

0.0207

64.6876%

0.8945%

GPU72

2⁶²

0.3125

66.1290%

8000

100000

0.0010

1.1954%

0.3135

66.5339%

0.4049%

Difference

+14.8025

+2.5277%

-8000

-100000

-0.0010

-1.1954%

+14.8015

+2.1228%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1965851	141541273	9	27.077	36 2² × 3²	-	9	9	9.166e-12	7.080e-7	1.441e-6
1965851	101972623073	12	36.569	25936 2⁴ × 1621	2008-07-15	16	1621	7.515e-9	8.137e-6	1.297e-5
1965851	5091416480431	13	42.211	1294965 3² × 5 × 7 × 4111	2008-07-15	9	4111	3.861e-7	1.829e-5	3.294e-5
1965851	26292181525352159	17	54.545	6687226429 13 × 514402033	2015-07-21	13	514402033	0.0020	2.2046	4.1176

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1965851

141541273

27.077

36
2² × 3²

9.166e-12

7.080e-7

1.441e-6

1965851

101972623073

36.569

25936
2⁴ × 1621

2008-07-15

1621

7.515e-9

8.137e-6

1.297e-5

1965851

5091416480431

42.211

1294965
3² × 5 × 7 × 4111

2008-07-15

4111

3.861e-7

1.829e-5

3.294e-5

1965851

26292181525352159

54.545

6687226429
13 × 514402033

2015-07-21

514402033

0.0020

2.2046

4.1176

exponent	prime factors	composite factor	digits	bits*
1965851	141541273 101972623073	14433334880901591929	20	63.646
1965851	141541273 5091416480431	720645570013383328663	21	69.288
1965851	101972623073 5091416480431	519185093666650643584463	24	78.781
1965851	141541273 26292181525352159	3721428843045426358158407	25	81.622
1965851	101972623073 26292181525352159	2681082716451629903293764607	28	91.115
1965851	5091416480431 26292181525352159	133864446324661450373607100529	30	96.757
1965851	141541273 101972623073 5091416480431	73486119080201969739214176041399	32	105.857
1965851	141541273 101972623073 26292181525352159	379483860704861739437066335437124711	36	118.192
1965851	141541273 5091416480431 26292181525352159	18947344142232752979906674610713633417	38	123.833
1965851	101972623073 5091416480431 26292181525352159	13650508727940542263281331889640135905617	41	133.326
1965851	141541273 101972623073 5091416480431 26292181525352159	1932110382450315020255140872795160347974038030441	49	160.403

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	101972623073	36.569	12	2.85862e-9	0.236	6.33237e-9
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	5091416480431	42.211	13	8.80569e-8	0.236	1.95061e-7
2014-11-30T12:05:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	26292181525352159	54.545	17	0.001	0.234	0.002

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.019 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:	21.019 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	10.604	0.002%
25	50000	1.002	36.699%
30	250000	0.064	93.809%
35	1000000	0.003	99.700%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	29	2.020
50000	6313162	7	0.539
50000	6750000	7	0.556
50000	6950000	1	0.081
50000	7500000	213	17.82

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-07-13T15:12:00	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-24T12:39:17	Oliver Kruse	ECM-HTC	50000	5000000						3	0.209
2021-01-07T05:02:29	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.488
2021-04-03T02:23:51	MarkS	desktop-i7	50000	5000000						11	0.766
2021-08-27T04:09:27	Dylan Delgado	colab	50000	6750000						7	0.556
2021-12-16T15:23:08	-Anonymous-	UMA2022	50000	6950000						1	0.081
2022-01-14T10:27:45	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.488
2022-05-19T15:18:43	debrouxl	z400	50000	6313162						7	0.539
2022-06-24T08:50:45	TJAOI	Manual testing	50000	7500000						213	17.82

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T09:23:53

Oliver Kruse

GTX-2

141541273

101972623073

5091416480431

26292181525352159

FCA2A6B2DC514C2C

2017-10-05T21:33:53

Oliver Kruse

Manual testing

141541273

101972623073

5091416480431

26292181525352159

FCA2A6B2DC514C__

2017-11-15T13:29:37

kkmrkkblmbrbk

c4.xlarge

141541273

101972623073

5091416480431

26292181525352159

FCA2A6B2DC514C__

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

10⁰

10¹

10²

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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