M54039893 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	2⁶⁸	1.1030	61.7647%	-	-	-	-	1.1030	61.7647%	0.0000%
PrimeNet	2⁶⁹	2.2092	62.3188%	240000	10000000	2.2109	5.3438%	4.4201	64.3325%	2.0136%
GPU72	2⁷³	35.3969	64.3836%	360000	12000000	2.8481	3.9213%	38.2450	65.7802%	1.3966%
Difference	-5	-34.2939	-2.6189%	-360000	-12000000	-2.8481	-3.9213%	-37.1420	-4.0155%	-4.0155%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

1.1030

61.7647%

1.1030

61.7647%

0.0000%

PrimeNet

2⁶⁹

2.2092

62.3188%

240000

10000000

2.2109

5.3438%

4.4201

64.3325%

2.0136%

GPU72

2⁷³

35.3969

64.3836%

360000

12000000

2.8481

3.9213%

38.2450

65.7802%

1.3966%

Difference

-5

-34.2939

-2.6189%

-360000

-12000000

-2.8481

-3.9213%

-37.1420

-4.0155%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
54039893	324239359	9	28.272	3 3	-	1	3	6.622e-13	3.177e-6	5.830e-6
54039893	18772918429271	14	44.094	173695 5 × 34739	2008-09-30	5	34739	6.923e-8	0.0054	0.0101
54039893	23566783395007607	17	54.388	218049871 13 × 17 × 19 × 51929	2015-08-07	19	51929	8.623e-5	0.0082	0.0151
54039893	67609521312420099409	20	65.874	625551953928 2³ × 3 × 11 × 29² × 31 × 90887	2019-06-20	841	90887	0.2496	0.0165	0.0265

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

54039893

324239359

28.272

3
3

6.622e-13

3.177e-6

5.830e-6

54039893

18772918429271

44.094

173695
5 × 34739

2008-09-30

34739

6.923e-8

0.0054

0.0101

54039893

23566783395007607

54.388

218049871
13 × 17 × 19 × 51929

2015-08-07

51929

8.623e-5

0.0082

0.0151

54039893

67609521312420099409

65.874

625551953928
2³ × 3 × 11 × 29² × 31 × 90887

2019-06-20

841

90887

0.2496

0.0165

0.0265

exponent	prime factors	composite factor	digits	bits*
54039893	324239359 18772918429271	6086919038066115877289	22	72.366
54039893	324239359 23566783395007607	7641278741689110293803913	25	82.660
54039893	324239359 67609521312420099409	21921667852635931771090438831	29	94.146
54039893	18772918429271 23566783395007607	442417302314776090345536464497	30	98.481
54039893	18772918429271 67609521312420099409	1269228028640121731060893955400839	34	109.968
54039893	23566783395007607 67609521312420099409	1593338944209954911644894093251204263	37	120.261
54039893	324239359 18772918429271 23566783395007607	143449102513052215762162831759633537423	39	126.754
54039893	324239359 18772918429271 67609521312420099409	411533682431106711761154646066142625422201	42	138.240
54039893	324239359 23566783395007607 67609521312420099409	516623197940372541970642096418656696213187417	45	148.534
54039893	18772918429271 23566783395007607 67609521312420099409	29911622029834260259958396808004543334587139182273	50	164.355
54039893	324239359 18772918429271 23566783395007607 67609521312420099409	96985251536037394229280839476950391998942565381039 81683007	58	192.628

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T05:44:00	markr	Manual testing	?	?	18772918429271	44.094	14	2.58612e-8	219.8	5.32333e-8
2014-11-20T12:17:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	23566783395007607	54.388	17	4.18231e-5	219.8	8.60896e-5
2019-06-20T11:37:08	TJAOI	Manual testing	2⁶⁵	2⁶⁶*	67609521312420099409	65.874	20	0.115	219.5	0.236
2022-08-10T19:29:26	LordJulius	Manual testing	2¹	2⁶⁶	18772918429271	44.094	14	6.92292e-8	219.8	1.42503e-7
2022-08-10T19:29:26	LordJulius	Manual testing	2¹	2⁶⁶	23566783395007607	54.388	17	8.62319e-5	219.8	0.000
2022-08-10T19:29:26	LordJulius	Manual testing	2¹	2⁶⁶	324239359	28.272	9	6.62172e-13	219.8	1.36303e-12
2022-08-10T19:29:26	LordJulius	Manual testing	2¹	2⁶⁶	67609521312420099409	65.874	20	0.250	219.5	0.513
2022-08-10T19:29:26	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	0.277	-	-
2022-08-10T19:29:26	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	0.553	-	-

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

10⁰

10¹

10²

10³

10⁴

10⁵

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