M2144621 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	13.8551	67.1642%	500000	15000000	0.1230	5.1662%	13.9781	68.8605%	1.6964%
PrimeNet	2⁵⁸	0.0179	62.0690%	9000	170000	0.0017	2.7324%	0.0196	63.1054%	1.0364%
GPU72	2⁶²	0.2865	64.5161%	10000	150000	0.0017	1.4882%	0.2881	65.0442%	0.5281%
Difference	+5	+13.5686	+2.6481%	+490000	+14850000	+0.1213	+3.6780%	+13.6899	+3.8164%	+3.8164%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.8551

67.1642%

500000

15000000

0.1230

5.1662%

13.9781

68.8605%

1.6964%

PrimeNet

2⁵⁸

0.0179

62.0690%

9000

170000

0.0017

2.7324%

0.0196

63.1054%

1.0364%

GPU72

2⁶²

0.2865

64.5161%

10000

150000

0.0017

1.4882%

0.2881

65.0442%

0.5281%

Difference

+13.5686

+2.6481%

+490000

+14850000

+0.1213

+3.6780%

+13.6899

+3.8164%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2144621	4765347863	10	32.150	1111 11 × 101	-	11	101	3.309e-10	1.516e-6	2.134e-6
2144621	67426884241	11	35.973	15720 2³ × 3 × 5 × 131	2008-07-14	8	131	2.994e-9	1.402e-6	1.552e-6
2144621	1721096955679	13	40.646	401259 3 × 59 × 2267	2008-07-14	59	2267	1.265e-7	1.709e-5	2.196e-5
2144621	126265257093273620743	21	66.775	29437662200751 3³ × 7 × 353 × 12917 × 34159	2016-03-14	12917	34159	7.8682	0.0013	0.0025
2144621	227260599484327429121	21	67.623	52983860431360 2⁹ × 5 × 20696820481	2018-01-09	512	20696820481	24.112	107.50	200.79

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2144621

4765347863

32.150

1111
11 × 101

101

3.309e-10

1.516e-6

2.134e-6

2144621

67426884241

35.973

15720
2³ × 3 × 5 × 131

2008-07-14

131

2.994e-9

1.402e-6

1.552e-6

2144621

1721096955679

40.646

401259
3 × 59 × 2267

2008-07-14

2267

1.265e-7

1.709e-5

2.196e-5

2144621

126265257093273620743

66.775

29437662200751
3³ × 7 × 353 × 12917 × 34159

2016-03-14

12917

34159

7.8682

0.0013

0.0025

2144621

227260599484327429121

67.623

52983860431360
2⁹ × 5 × 20696820481

2018-01-09

512

20696820481

24.112

107.50

200.79

exponent	prime factors	composite factor	digits	bits*
2144621	4765347863 67426884241	321312558726597726983	21	68.123
2144621	4765347863 1721096955679	8201625699760728363977	22	72.796
2144621	67426884241 1721096955679	116048205198105440554639	24	76.619
2144621	4765347863 126265257093273620743	601697873060577040281927522209	30	98.925
2144621	4765347863 227260599484327429121	1082975812096738616354041318423	31	99.773
2144621	67426884241 126265257093273620743	8513672873688264565577197411063	31	102.748
2144621	67426884241 227260599484327429121	15323474133970009857082799382161	32	103.596
2144621	1721096955679 126265257093273620743	217314749591259489208934926049497	33	107.421
2144621	1721096955679 227260599484327429121	391137525918260455532989750928159	33	108.269
2144621	4765347863 67426884241 1721096955679	553010066645777252795722493386457	33	108.769
2144621	126265257093273620743 227260599484327429121	28695118021060089276240327093264367856903	41	134.398
2144621	4765347863 67426884241 126265257093273620743	40570612834911440475751921044338199608369	41	134.898
2144621	4765347863 67426884241 227260599484327429121	73021684718049762178538453449838641671943	41	135.745
2144621	4765347863 1721096955679 126265257093273620743	1035580377563088530380269610356033561174911	43	139.571
2144621	4765347863 1721096955679 227260599484327429121	1863906373273689574451539235586404757174217	43	140.419
2144621	67426884241 1721096955679 126265257093273620743	14652856464551755644283643921641329655276777	44	143.394
2144621	67426884241 1721096955679 227260599484327429121	26373184682401684963310827892472399200242319	44	144.242
2144621	4765347863 126265257093273620743 227260599484327429121	13674221934019148542712105938830835706093860084828 9	51	166.548
2144621	67426884241 126265257093273620743 227260599484327429121	19348224010878516397341820066135125422974398337656 23	52	170.371
2144621	1721096955679 126265257093273620743 227260599484327429121	49387080268896130661665181426988486624842134805202 137	53	175.044
2144621	4765347863 67426884241 1721096955679 126265257093273620743	69825958240197444012385250727846449725251715950477 551	53	175.544
2144621	4765347863 67426884241 1721096955679 227260599484327429121	12567739926678720314751248710215414131535764392881 4297	54	176.392
2144621	4765347863 67426884241 126265257093273620743 227260599484327429121	92201017943085226866683301132687538603608020222060 86805913649	61	202.520
2144621	4765347863 1721096955679 126265257093273620743 227260599484327429121	23534661741919364161753494833460687526329554980632 7924835983231	63	207.194
2144621	67426884241 1721096955679 126265257093273620743 227260599484327429121	33300169442918345549769089243778158808930074184096 81576104823017	64	211.017
2144621	4765347863 67426884241 1721096955679 126265257093273620743 227260599484327429121	15868689129234883844908768957129453512620955432961 722957201590228054162671	74	243.167

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-14T01:06:55	alpertron	Manual testing	500000	15000000	12		126265257093273620743	21	66.775	0.048	0.282	0.095	5.166%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-14T01:06:55

alpertron

Manual testing

500000

15000000

126265257093273620743

66.775

0.048

0.282

0.095

5.166%

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.699 GHz-days
Estimated T-Level:	1.250

Digits	B1	Curves	Complete	FacMiss
20	11000	25 / 100	0.250	77.782%
25	50000	25 / 280	0.089	91.444%

New Calculation Method

Total ECM effort:	2.699 GHz-days
Estimated T-Level:	1.250

Digits	B1	Complete	FacMiss
20	11000	1.049	35.044%
25	50000	0.096	90.806%
30	250000	0.006	99.394%

ECM Summary

B1	B2	factor	curves	GHz-days
		67426884241	1	0.00000e+0
		1721096955679	1	0.00000e+0
50000	50000		7	0.355
50000	5000000		10	0.853
50000	5000000	227260599484327429121	1	0.085
50000	7150000		14	1.405

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

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-14T20:20:00	George Woltman	Manual testing			1721096955679	40.646		1		1	-
2008-07-14T20:20:00	George Woltman	Manual testing			67426884241	35.973		1		1	-
2018-01-09T12:19:48	ATH	ec2-1xd	50000	5000000	227260599484327429121	67.623	1	2		1	0.085
2018-08-08T01:04:59	ATH	ec2-ECMCF	50000	5000000						3	0.256
2021-12-29T07:35:19	JackBlock	school1	50000	50000						7	0.355
2022-01-17T04:54:11	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.597
2022-05-18T16:12:21	debrouxl	dl380g9-1	50000	7150000						7	0.702
2022-07-15T18:00:10	debrouxl	dl380g9-1	50000	7150000						7	0.702