M261168067 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	0.1138	58.2090%	-	-	-	-	0.1138	58.2090%	0.0000%
PrimeNet	2⁷⁶	58.5983	63.1579%	1000000	65000000	74.0961	5.4780%	132.6944	65.1761%	2.0182%
GPU72	2⁸⁰	937.5823	65.0000%	1600000	65000000	83.4646	4.0518%	1,021.0469	66.4181%	1.4181%
Difference	-13	-937.4685	-6.7910%	-1600000	-65000000	-83.4646	-4.0518%	-1,020.9331	-8.2092%	-8.2092%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

0.1138

58.2090%

0.1138

58.2090%

0.0000%

PrimeNet

2⁷⁶

58.5983

63.1579%

1000000

65000000

74.0961

5.4780%

132.6944

65.1761%

2.0182%

GPU72

2⁸⁰

937.5823

65.0000%

1600000

65000000

83.4646

4.0518%

1,021.0469

66.4181%

1.4181%

Difference

-13

-937.4685

-6.7910%

-1600000

-65000000

-83.4646

-4.0518%

-1,020.9331

-8.2092%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
261168067	40017738234143	14	45.186	76613 23 × 3331	2008-01-28	23	3331	2.841e-8	0.0034	0.0056
261168067	81828569186171623	17	56.183	156658833 3³ × 109 × 53231	2015-03-16	109	53231	6.757e-5	0.0496	0.0895
261168067	5108828184008408681	19	62.148	9780729020 2² × 5 × 61 × 8016991	2016-07-04	61	8016991	0.0058	7.2140	13.472
261168067	200921966730704861783	21	67.445	384660286073 7 × 409 × 4733 × 28387	2022-08-05	4733	28387	0.1344	0.0994	0.1591

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

261168067

40017738234143

45.186

76613
23 × 3331

2008-01-28

3331

2.841e-8

0.0034

0.0056

261168067

81828569186171623

56.183

156658833
3³ × 109 × 53231

2015-03-16

109

53231

6.757e-5

0.0496

0.0895

261168067

5108828184008408681

62.148

9780729020
2² × 5 × 61 × 8016991

2016-07-04

8016991

0.0058

7.2140

13.472

261168067

200921966730704861783

67.445

384660286073
7 × 409 × 4733 × 28387

2022-08-05

4733

28387

0.1344

0.0994

0.1591

exponent	prime factors	composite factor	digits	bits*
261168067	40017738234143 81828569186171623	3274594261766675907206556324089	31	101.369
261168067	40017738234143 5108828184008408681	204443748950860645881464411795383	33	107.333
261168067	40017738234143 200921966730704861783	8040442670118535770385735306456969	34	112.631
261168067	81828569186171623 5108828184008408681	418048100515395600978395578789059263	36	118.331
261168067	81828569186171623 200921966730704861783	16441157055645155843653006579131783809	38	123.629
261168067	5108828184008408681 200921966730704861783	1026475806420224824786946002159882338223	40	129.593
261168067	40017738234143 81828569186171623 5108828184008408681	16729339455705802525282250132223406857613797016609	50	163.517
261168067	40017738234143 81828569186171623 200921966730704861783	65793791931924110400039870489641791139885729839068 7	51	168.814
261168067	40017738234143 5108828184008408681 200921966730704861783	41077240125005399682070612084671503305556729892547 889	53	174.779
261168067	81828569186171623 5108828184008408681 200921966730704861783	83995046543588676922078596892490447380628893283010 845929	56	185.776
261168067	40017738234143 81828569186171623 5108828184008408681 200921966730704861783	33612917855459894356898712864175458029791841476720 78843509097100353847	70	230.962

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-03-16T12:10:00	TJAOI	Manual testing	2⁵⁶	2⁵⁷*	81828569186171623	56.183	17	3.08126e-5	6,108	6.32691e-5
2022-07-04T01:49:34	LordJulius	Manual testing	2¹	2⁶²	40017738234143	45.186	14	2.84084e-8	6,108	5.83324e-8
2022-07-04T01:49:34	LordJulius	Manual testing	2¹	2⁶²	81828569186171623	56.183	17	6.75682e-5	6,108	0.000
2016-07-04T16:33:07	TJAOI	Manual testing	2⁶²	2⁶³*	5108828184008408681	62.148	19	0.003	6,108	0.007
TF assumed completed to 67 but no detailed record exists
2022-08-05T09:32:55	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	200921966730704861783	67.445	21	0.021	6,107	0.042

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

10³

10⁴

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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