M2174611 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	13.6640	67.1642%	500000	15000000	0.1230	5.1748%	13.7870	68.8634%	1.6992%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8570%	0.0195	63.1526%	1.0837%
GPU72	2⁶²	0.2825	64.5161%	11000	160000	0.0018	1.5680%	0.2843	65.0725%	0.5564%
Difference	+5	+13.3815	+2.6481%	+489000	+14840000	+0.1212	+3.6069%	+13.5027	+3.7909%	+3.7909%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.6640

67.1642%

500000

15000000

0.1230

5.1748%

13.7870

68.8634%

1.6992%

PrimeNet

2⁵⁸

0.0177

62.0690%

10000

180000

0.0018

2.8570%

0.0195

63.1526%

1.0837%

GPU72

2⁶²

0.2825

64.5161%

11000

160000

0.0018

1.5680%

0.2843

65.0725%

0.5564%

Difference

+13.3815

+2.6481%

+489000

+14840000

+0.1212

+3.6069%

+13.5027

+3.7909%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2174611	1208631396913	13	40.137	277896 2³ × 3 × 11579	-	8	11579	7.750e-8	6.087e-5	0.0001
2174611	8139621341982103	16	52.854	1871512041 3 × 7 × 89119621	2014-08-27	7	89119621	0.0003	0.4629	0.8646
2174611	323755815230463484146287	24	78.099	74439937816571213 41047 × 1813529315579	2022-06-04	41047	1813529315579	42,000	9,419.9	17,594

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2174611

1208631396913

40.137

277896
2³ × 3 × 11579

11579

7.750e-8

6.087e-5

0.0001

2174611

8139621341982103

52.854

1871512041
3 × 7 × 89119621

2014-08-27

89119621

0.0003

0.4629

0.8646

2174611

323755815230463484146287

78.099

74439937816571213
41047 × 1813529315579

2022-06-04

41047

1813529315579

42,000

9,419.9

17,594

exponent	prime factors	composite factor	digits	bits*
2174611	1208631396913 8139621341982103	9837801912902696841135448039	28	92.990
2174611	1208631396913 323755815230463484146287	391301443220702201876163886052212031	36	118.236
2174611	8139621341982103 323755815230463484146287	2635249743240694966283616710281387901561	40	130.953
2174611	1208631396913 8139621341982103 323755815230463484146287	31850455783876257366882951006932634687680891632811 93	52	171.090

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T13:45:56	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1208631396913	-	-	0.123	-	-	5.175%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-08-27T11:13:00	TJAOI	Manual testing	?	?	8139621341982103	52.854	16	5.14166e-5	0.308	0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.125 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	4.125 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	1.026	35.834%
25	50000	0.097	90.779%
30	250000	0.006	99.384%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		10	0.855
50000	7150000	323755815230463484146287	7	0.704
50000	45039225		7	2.566

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-14T05:02:49	Oliver Kruse	O2.261	50000	5000000						3	0.256
2022-03-05T09:59:46	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.598
2022-06-04T18:44:52	debrouxl	o9020	50000	7150000	323755815230463484146287	78.099	7	2	2018705950136607	7	0.704
2022-08-06T14:55:52	Stef42	AMD-DESKTOP	50000	45039225						7	2.566

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-10T16:06:25

kkmrkkblmbrbk

old

1208631396913

8139621341982103

EE71C3E07A55EF__

2017-10-22T19:28:54

Oliver Kruse

GTX-0

1208631396913

8139621341982103

EE71C3E07A55EF__

2022-06-10T15:53:14

XZT

800G5Mini1

1208631396913

8139621341982103

323755815230463484146287

BAE25D633EEAFAF7

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

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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