M14 087 Mersenne number exponent details

is 2 ¹⁴⁰⁸⁷ - 1

has 4241 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	2,109.3148	79.1045%	7800000000	32022192391138950	498,925.6566	36.6106%	501,034.9714	86.7544%
Target	2⁴⁴	0.0002	68.1818%	500	80000	0.0000	1.4032%	0.0002	68.6283%
Difference	+23	+2,109.3146	+10.9227%	+7799999500	+32022192391058950	+498,925.6566	+35.2074%	+501,034.9712	+18.1262%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
14087	22229287	8	24.406	789 3 × 263	-	3	263	1.858e-10	4.909e-9	7.613e-9
14087	2003875751	10	30.900	71125 5³ × 569	2008-08-26	125	569	1.417e-8	4.266e-8	7.275e-8
14087	192765903726414617	18	57.420	6841978552084 2² × 13 × 433 × 439 × 692191	2008-08-26	439	692191	2.1074	1.090e-5	2.014e-5
14087	1282966012383402698574287	25	80.086	45537233349307968289 7² × 109 × 197 × 21407 × 2021724751	2010-04-08	21407	2021724751	30,208,599	0.0315	0.0588
14087	42864457068925853644401683829426471408313	41	134.977	1521418934795409016980254270938683588 2² × 3 × 43 × 1613 × 6863 × 2358203 × 23989783 × 4708073584103	2023-05-23	23989783	4708073584103	1.100e+13	73.361	137.01

exponent	prime factors	composite factor	digits	bits*
14087	22229287 2003875751	44544729181319537	17	55.306
14087	22229287 192765903726414617	4285048597748840002288079	25	81.826
14087	2003875751 192765903726414617	386278920096962789178252367	27	88.320
14087	22229287 1282966012383402698574287	28519419700516212623182316543369	32	104.492
14087	2003875751 1282966012383402698574287	2570904481572266382540975991414537	34	110.986
14087	22229287 2003875751 192765903726414617	8586704976885453668963866024472329	34	112.726
14087	22229287 2003875751 1282966012383402698574287	57149373570456120657955144573263278945119	41	135.392
14087	192765903726414617 1282966012383402698574287	247312102827361067912815974577768137153079	42	137.505
14087	22229287 42864457068925853644401683829426471408313	952846318284331582381400973127580078332683862831	48	159.383
14087	22229287 192765903726414617 1282966012383402698574287	5497571712322920631260477277073911740231156024673	49	161.911
14087	2003875751 42864457068925853644401683829426471408313	85895046100201053734991511129356526292613240518063	50	165.877
14087	2003875751 192765903726414617 1282966012383402698574287	49558272578456738331195611358182203374149718308732 9	51	168.406
14087	22229287 2003875751 42864457068925853644401683829426471408313	19093856316395999811775482434581603482815457034760 51111081	58	190.283
14087	192765903726414617 42864457068925853644401683829426471408313	82628058046335935824456480545959950862350607093701 38511121	58	192.397
14087	22229287 2003875751 192765903726414617 1282966012383402698574287	11016450643707448534480482980214919970963424692539 782404423	59	192.811
14087	1282966012383402698574287 42864457068925853644401683829426471408313	54993641558699360087001539134683128157782943989672 903814139847831	65	215.063
14087	22229287 192765903726414617 42864457068925853644401683829426471408313	18367628165646608158554247250660604382250891397101 2398193461400727	66	216.802
14087	2003875751 192765903726414617 42864457068925853644401683829426471408313	16557636187127301619852053412085238655021592041519 679045946615726871	68	223.297
14087	22229287 1282966012383402698574287 42864457068925853644401683829426471408313	12224694413834554220903021828666029098771383456513 64015007909335571626497	73	239.469
14087	2003875751 1282966012383402698574287 42864457068925853644401683829426471408313	11020042477866349077755963457166904358420654338229 6726374910251991370846081	75	245.963
14087	22229287 2003875751 192765903726414617 42864457068925853644401683829426471408313	36806444684523849324325619283657203852596896068785 6861660233507671329070977	75	247.703
14087	22229287 2003875751 1282966012383402698574287 42864457068925853644401683829426471408313	24496768699268222129162262765087532388488359201230 24649748349590758504060967374247	82	270.369
14087	192765903726414617 1282966012383402698574287 42864457068925853644401683829426471408313	10600899014269194722990888929431341547131111633265 532805755506314851543139594145727	83	272.482
14087	22229287 192765903726414617 1282966012383402698574287 42864457068925853644401683829426471408313	23565042664620702475624996839745203804620150712489 8275947054401703147314842919328885306649	90	296.888
14087	2003875751 192765903726414617 1282966012383402698574287 42864457068925853644401683829426471408313	21242884473493842291698604519621815545694858219574 806133548452339058378462363116603895565977	92	303.382
14087	22229287 2003875751 192765903726414617 1282966012383402698574287 42864457068925853644401683829426471408313	47221417566913851303490599736617046922631261778723 7383512008875450750004594488417202459854130168399	99	327.788

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-02-06	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 22229287 skipped known factor: 2003875751	-	-	1.42986e-5	-	-	0.207%
2023-02-11	USAFSS	6917th_Scty_Sq	30000000	2010341563230		-	skipped known factor: 22229287 skipped known factor: 2003875751 skipped known factor: 192765903726414617 skipped known factor: 1282966012383402698574287	-	-	31.33	-	-	17.949%
2023-05-23	JacobZ	GreatLakes	7800000000	32022192391138950			42864457068925853644401683829426471408313	41	134.977	498,926	5.55654e-6	997,851	36.611%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	2003875751	30.900	10	4.01112e-9	0.000	2.48604e-7

ECM factoring results:

Total ECM effort:	369.405 GHz-days
Estimated T-Level:	39.146

Digits	B1	Complete	FacMiss
20	11000	911.588	0.000%
25	50000	213.664	0.000%
30	250000	41.476	0.000%
35	1000000	6.432	0.161%
40	3000000	0.829	43.641%
45	11000000	0.092	91.201%
50	44000000	0.009	99.107%

ECM Summary

B1	B2	factor	curves	GHz-days
		192765903726414617	1	0.00000e+0
		1282966012383402698574287	1	0.00000e+0
50000	5000000		148	0.030
250000	25000000		545	0.561
500000	50000000		10	0.021
1000000	100000000		1,421	5.848
3000000	300000000		1,258	15.53
3000000	22972799850		800	252.7
3000000	22972874925		100	31.58
3000000	22973231148		200	63.17

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			192765903726414617	57.420		1		1	-
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.010
2009-06-08	unconnected	dual5430	250000	25000000						30	0.031
2009-06-10	Rob_Dee	twopc	50000	5000000						80	0.016
2009-07-06	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-06	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-08	Rob_Dee	twopc	250000	25000000						10	0.010
2009-08-05	Rob_Dee	twopc	500000	50000000						5	0.010
2009-08-12	Rob_Dee	twopc	500000	50000000						5	0.010
2010-04-08	James Hintz	17_012210			1282966012383402698574287	80.086		1		1	-
2010-04-09	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-09	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-09	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-11	James Hintz	17_012210	250000	25000000						11	0.011
2010-04-11	James Hintz	17_012210	250000	25000000						11	0.011
2011-02-06	BloodIce	Mjolnir	250000	25000000						40	0.041
2011-02-06	BloodIce	Mjolnir	250000	25000000						40	0.041
2011-02-06	BloodIce	Mjolnir	250000	25000000						100	0.103
2011-04-09	James Hintz	17_051310	250000	25000000						11	0.011
2013-03-17	BloodIce	Mjolnir4	250000	25000000						215	0.221
2014-08-11	James Hintz	08_04_2014	1000000	100000000						11	0.045
2017-05-04	kkmrkkblmbrbk	c4.large	1000000	100000000						1410	5.802
2019-03-10	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-12	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-14	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-16	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-19	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-21	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-24	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-29	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-31	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-02	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-04	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-06	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-08	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-17	storm5510	HP-Z220-CMT	3000000	300000000						3	0.037
2019-04-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-28	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-01	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-05-04	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-06	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-09	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-12	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-14	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-16	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-23	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-27	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-31	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-04	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-08	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-12	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-16	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-28	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-07-08	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-23	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-15	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-07	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-12	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-25	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-03	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-16	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-21	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2021-10-22	nordi	sweet16	3000000	300000000						1000	12.35
2023-06-19	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-19	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-19	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-21	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-23	Denial140	i5-8400	3000000	22973231148						200	63.17
2023-08-01	Denial140	i5-8400	3000000	22972874925						100	31.58

Lucas-Lehmer results:
No L-L results for M14087

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

22229287

2003875751

192765903726414617

1282966012383402698574287

58F06FB695492A7F

2017-09-21

Oliver Kruse

Manual testing

22229287

2003875751

192765903726414617

1282966012383402698574287

58F06FB695492A7F

2017-10-02

kkmrkkblmbrbk

Manual testing

22229287

2003875751

192765903726414617

1282966012383402698574287

58F06FB695492A__

2017-12-07

ATH

Manual testing

22229287

2003875751

192765903726414617

1282966012383402698574287

58F06FB695492A__

2020-04-17

Oliver Kruse

Manual testing

22229287

2003875751

192765903726414617

1282966012383402698574287

800E03E8C2825C__

2023-05-23

JacobZ

GreatLakes

22229287

2003875751

192765903726414617

1282966012383402698574287

42864457068925853644401683829426471408313

800E03E8C2825C98

2023-06-19

Denial140

i5-8400

22229287

2003875751

192765903726414617

1282966012383402698574287

42864457068925853644401683829426471408313

800E03E8C2825C98

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 = 7800000000, B2 = 32022192391138950 (P-1 stage 2)

B1 = 30000000, B2 = 2010341563230 (P-1 stage 2)

B1 = 7800000000 (P-1 stage 1)

B1 = 30000000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=39.15 ~= 113-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2023-08-01T08:23:52+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	<	146M	PrimeNet wavefront