M1381 Mersenne number exponent details

is 2 ¹³⁸¹ - 1

has 416 decimal digits

takes 0.000 GHz-days to do one PRP test

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶³	1,155.6963	82.5397%	1000000000	100000000000	0.1512	18.2043%	1,155.8474	100.7440%	28.2440%
PrimeNet	2⁴⁰	0.0001	72.5000%	500	10000	0.0000	1.7523%	0.0001	74.2523%	1.7523%
GPU72	2⁴⁴	0.0017	75.0000%	500	10000	0.0000	0.6737%	0.0017	75.6737%	0.6737%
Difference	+19	+1,155.6946	+7.5397%	+999999500	+99999990000	+0.1512	+17.5305%	+1,155.8457	+25.0702%	+25.0702%

Remaining cofactor is not a probable-prime

	GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
1381	8287	4	13.017	3 3	1	3	-	7.906e-13	2.622e-11	4.812e-11
1381	462853283623	12	38.752	167579031 3 × 19 × 37 × 181 × 439	181	439	-	4.024e-5	4.612e-9	8.709e-9
1381	20314602484365657521	20	64.139	7355033484563960 2³ × 5 × 13 × 14144295162623	13	14144295162623	-	3,818.9	18.220	34.030
1381	324347780588879609356756802551	30	98.033	117432215998870242344951775 3 × 5² × 97 × 85133 × 189607853131799057	85133	189607853131799057	-	9.070e+13	244,241	456,175
1381	57179431575531817052111791127393011679057816412043 56084154399	61	201.831	20702183771010795456955753485660033192997037078944 08430179 3 × 11 × 251 × 1797017 × 2131849 × 175645475683 × 371435068600254922310844406067	175645475683	371435068600254922310844406067	2020-10-22	1.205e+14	4.785e+17	8.936e+17

exponent	prime factors	composite factor	digits	bits*
1381	8287 462853283623	3835665161383801	16	51.768
1381	8287 20314602484365657521	168347110787938203876527	24	77.156
1381	462853283623 20314602484365657521	9402680465384598103808296078583	31	102.891
1381	8287 324347780588879609356756802551	2687870057740045322739443622740137	34	111.050
1381	8287 462853283623 20314602484365657521	77920013016642164486259349603217321	35	115.908
1381	462853283623 324347780588879609356756802551	150125435281395267789404400922572612922273	42	136.785
1381	8287 462853283623 324347780588879609356756802551	1244089482176922584170794270445359243286876351	46	149.802
1381	20314602484365657521 324347780588879609356756802551	6588996229349340900407703021411282233704685136071	49	162.173
1381	8287 20314602484365657521 324347780588879609356756802551	54603011752617988041678634938435295870710725722620 377	53	175.189
1381	462853283623 20314602484365657521 324347780588879609356756802551	30497385405339080405245207629032302574490155993097 82910865233	61	200.924
1381	8287 462853283623 20314602484365657521 324347780588879609356756802551	25273183285404495931826703562179069143479992271480 170982340185871	65	213.941
1381	8287 57179431575531817052111791127393011679057816412043 56084154399	47384594946643216791085041307270588778435212460660 498869387504513	65	214.848
1381	462853283623 57179431575531817052111791127393011679057816412043 56084154399	26465687660431549865081646629789772559275098949178 66249922201696470107577	73	240.583
1381	8287 462853283623 57179431575531817052111791127393011679057816412043 56084154399	21932115364199625373193160562106784519871274499184 357613105285458647781490599	77	253.600
1381	20314602484365657521 57179431575531817052111791127393011679057816412043 56084154399	11615774227389147735099618379621279608581412519070 0441735273563265060280919584879	81	265.970
1381	8287 20314602484365657521 57179431575531817052111791127393011679057816412043 56084154399	96259921022373867280770537511921544116314165545533 4560660212018777554547980599892273	84	278.987
1381	324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	18546021726857448509659185337271164007883842296604 19699433058631960296768105757463841071849	91	299.865
1381	462853283623 20314602484365657521 57179431575531817052111791127393011679057816412043 56084154399	53763992429704828914263117380219118139969189533750 900520527960861416780130664675255209136617	92	304.722
1381	8287 324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	15369088205046767579954566888996613613333340111195 898049201756883054979317292412102850962412663	95	312.881
1381	8287 462853283623 20314602484365657521 57179431575531817052111791127393011679057816412043 56084154399	44554220526496391721249845372987583202592467366619 3712613615211658560856942818163839918115145079	96	317.739
1381	462853283623 324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	85840870544194708515314015659790929874004094665491 46081189058992811076124833044198704807955215180289 27	102	338.616
1381	8287 462853283623 324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	71136329419974154946640724777268743586587193249292 77357481373187342538784649143727466674352486819905 718049	106	351.633
1381	20314602484365657521 324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	37675505904751778533727941818837228840143462103796 71152559847001565254383954864603629724150497324638 6288226329	110	364.004
1381	8287 20314602484365657521 324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	31221691743267798870900345385270411539826887045416 33484126345210197126307983396297027952403517132928 03170531588423	114	377.020
1381	462853283623 20314602484365657521 324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	17438231620172086173085262126194310364418277193137 77158489254166696968812318805086814392187503390937 4659724239282253109967	122	402.756
1381	8287 462853283623 20314602484365657521 324347780588879609356756802551 57179431575531817052111791127393011679057816412043 56084154399	14451062543636607811635756723977224998993426309953 27131240044927941778054768593775443086805784060069 87805134770932031522296529	126	415.772

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-09-07T20:58:12	kkmrkkblmbrbk	Manual testing	1000000000	100000000000	12	-		-	-	0.151	-	-	18.204%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-10-25T00:00:00	Carsten Kossendey	v4_computers	?	?	8287 462853283623 324347780588879609356756802551	149.802	46	9.80931e+12	6.90948e-8	3.00992e+13

ECM factoring results:

ECM Summary

B1	B2	factor	curves	GHz-days
44000000	4400000000		14,189	212.4
110000000	11000000000		1,267	47.42
200000000	20000000000		231	15.72
200000000	2000000000000		438	989.5
800000000	3000000000000		3,660	12,823
800000000	16000123456789		3	53.67
850000000	15892628251516	57179431575531817052111791127393011679057816412043 56084154399	1	17.78

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-07T18:13:00	Matthias Wurtinger	AMD_Funzel	110000000	11000000000						200	7.485
2009-07-08T09:43:00	Matthias Wurtinger	WUR_E6600	44000000	4400000000						100	1.497
2009-10-13T11:50:00	Carsten Kossendey	durandal	44000000	4400000000						1	0.015
2010-12-30T10:03:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2010-12-30T23:24:00	ANONYMOUS	13_052010	44000000	4400000000						3	0.045
2011-01-01T13:24:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2011-01-04T06:47:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2011-01-06T08:48:00	James Hintz	13_052010	44000000	4400000000						3	0.045
2011-01-06T09:45:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2011-01-10T22:06:00	James Hintz	17_051310	44000000	4400000000						3	0.045
2011-01-11T12:26:00	James Hintz	NEW_OMFG	44000000	4400000000						3	0.045
2011-12-13T19:44:00	Michael Kenn	Manual testing	44000000	4400000000						14064	210.5
2013-04-01T21:41:00	Never Odd Or Even	Manual testing	200000000	20000000000						231	15.72
2013-05-07T20:07:00	Never Odd Or Even	Note	200000000	2000000000000						1	2.259
2013-05-12T17:42:00	Never Odd Or Even	Manual testing	200000000	2000000000000						437	987.3
2015-08-31T14:33:00	BloodIce	URM2	110000000	11000000000						1067	39.93
2017-08-25T08:58:07	Matthias Wurtinger	i5-750	800000000	3000000000000						1207	4,229
2017-08-25T08:58:08	Matthias Wurtinger	i5-750	800000000	3000000000000						1224	4,288
2017-08-25T08:58:09	Matthias Wurtinger	i5-750	800000000	3000000000000						1229	4,306
2020-10-22T23:48:27	Ryan Propper	Manual testing	850000000	15892628251516	57179431575531817052111791127393011679057816412043 56084154399	201.831	1	2	15369383506190878879	1	17.78
2021-01-03T14:38:04	Marcel PERRIN	Manual testing	800000000	16000123456789						3	53.67

Lucas-Lehmer results:
Exponent "1381" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-25T08:10:51

csaba

office

5F12ECA1920135__

2017-09-27T07:34:22

Oliver Kruse

Manual testing

8287

462853283623

20314602484365657521

324347780588879609356756802551

5F12ECA1920135__

2017-10-09T00:32:45

Chang Chia-Tche

homura

5F12ECA1920135__

2017-10-12T13:29:14

kkmrkkblmbrbk

Manual testing

8287

462853283623

20314602484365657521

324347780588879609356756802551

5F12ECA1920135__

2020-04-17T12:30:33

Oliver Kruse

IOS-1

8287

462853283623

20314602484365657521

324347780588879609356756802551

8B47394C9B3C899A

2020-08-12T10:14:42

_p95holder_

TFL16_PRPt11-E_b

8287

462853283623

20314602484365657521

324347780588879609356756802551

8B47394C9B3C899A

2020-10-23T01:26:04

James Heinrich

3930K

8287

462853283623

20314602484365657521

324347780588879609356756802551

57179431575531817052111791127393011679057816412043
56084154399

8B47394C9B3C899A

2020-10-23T11:38:11

ANONYMOUS

dory

8287

462853283623

20314602484365657521

324347780588879609356756802551

57179431575531817052111791127393011679057816412043
56084154399

8B47394C9B3C899A

2020-10-26T03:55:52

Klaus Nordmann

no1

8287

462853283623

20314602484365657521

324347780588879609356756802551

57179431575531817052111791127393011679057816412043
56084154399

8B47394C9B3C899A

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 = 1000000000, B2 = 100000000000 (stage 2)

B1 = 1000000000 (stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

10²⁵

10²⁶

10²⁷

10²⁸

10²⁹

10³⁰

TF factor-bounds graph:

2⁶³

2¹⁰

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

2¹⁶⁰

2¹⁷⁰

2¹⁸⁰

2¹⁹⁰

2²⁰⁰

2²¹⁰

Last modified: 2021-01-03T14:38:04+00:00

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	<	123M	PrimeNet wavefront