M14 033 Mersenne number exponent details

is 2 ¹⁴⁰³³ - 1

has 4225 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	2,117.4316	79.1045%	400000000	400000000	0.1144	7.8399%	2,117.5460	80.7427%
Target	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.4015%	0.0002	68.6278%
Difference	+23	+2,117.4314	+10.9227%	+399999500	+399990000	+0.1144	+6.4383%	+2,117.5458	+12.1149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
14033	84199	5	16.362	3 3	-	1	3	6.225e-13	3.171e-10	5.820e-10
14033	193445668956521	15	47.459	6892527220 2² × 5 × 41 × 79 × 103 × 1033	2008-08-26	103	1033	0.0013	4.395e-8	5.995e-8
14033	2332966266085570691423	22	70.983	83124287967133567 7² × 11 × 154219458195053	2008-08-29	49	154219458195053	20,152	2,402.8	4,487.8
14033	5213112341720972308927	22	72.143	185744756706369711 3 × 2017 × 30696538870661	2008-08-29	2017	30696538870661	103,425	478.27	893.27
14033	11421036014050568652027339573807169	35	113.137	406934939572812964156892310048 2⁵ × 3 × 1747 × 162008565247 × 14976932284007	2017-04-30	162008565247	14976932284007	1.092e+13	277.15	435.83

exponent	prime factors	composite factor	digits	bits*
14033	84199 193445668956521	16287931880470111679	20	63.820
14033	84199 2332966266085570691423	196433426638138966647125177	27	87.344
14033	84199 5213112341720972308927	438938846060564147439344473	27	88.504
14033	193445668956521 2332966266085570691423	451302219995920193365980268894619383	36	118.442
14033	193445668956521 5213112341720972308927	1008454004289709188125172032143162967	37	119.602
14033	84199 11421036014050568652027339573807169	961639811347043829932049964774989822631	39	129.499
14033	84199 193445668956521 2332966266085570691423	37999195621436484361222172660658057429217	41	134.803
14033	84199 193445668956521 5213112341720972308927	84910818707189223930951359934422178658433	41	135.963
14033	2332966266085570691423 5213112341720972308927	12162015234549382408993659906796720145233121	44	143.125
14033	84199 2332966266085570691423 5213112341720972308927	1024029520733823449454857170492377039508483555079	49	159.487
14033	193445668956521 11421036014050568652027339573807169	2209349951914530427866952235723805986871499099049	49	160.596
14033	84199 193445668956521 11421036014050568652027339573807169	18602505660125154749596951129570874028859335264082 6751	54	176.958
14033	2332966266085570691423 11421036014050568652027339573807169	26644891744528384631786166837859251003990843591804 211487	56	184.120
14033	5213112341720972308927 11421036014050568652027339573807169	59539143800086719543339917896401310100229463765795 297663	56	185.280
14033	193445668956521 2332966266085570691423 5213112341720972308927	23526891729068049332616375596681338364127836576083 58132041	58	190.584
14033	84199 2332966266085570691423 11421036014050568652027339573807169	22434732399975454576117634615809110752850250395863 22802993913	61	200.481
14033	84199 5213112341720972308927 11421036014050568652027339573807169	50131363688235016988296777469590939091292206196161 98267926937	61	201.641
14033	84199 193445668956521 2332966266085570691423 5213112341720972308927	19809407566958006857569662088649720089211997118696 6146359720159	63	206.946
14033	193445668956521 2332966266085570691423 11421036014050568652027339573807169	51543389077943772064248440734898665903626480340884 10719592144491756727	70	231.579
14033	193445668956521 5213112341720972308927 11421036014050568652027339573807169	11517589501506275286792794432849547834597713109837 653818400157799910423	71	232.739
14033	84199 193445668956521 2332966266085570691423 11421036014050568652027339573807169	43399018169737876640376544614377327704194460182221 0094178938974061424656673	75	247.940
14033	84199 193445668956521 5213112341720972308927 11421036014050568652027339573807169	96976951843732687287266649845149907812529284613522 0613855474886594657706177	75	249.100
14033	2332966266085570691423 5213112341720972308927 11421036014050568652027339573807169	13890281399722017027092179770219742285115152961362 9422754603265316505006044449	78	256.263
14033	84199 2332966266085570691423 5213112341720972308927 11421036014050568652027339573807169	11695478035751941116641344444727320806644107641937 983766514840336384405003936561351	83	272.624
14033	193445668956521 2332966266085570691423 5213112341720972308927 11421036014050568652027339573807169	26870147773635464528567242619974834391223053318336 637846777057816788412263421159383574401929	92	303.721
14033	84199 193445668956521 2332966266085570691423 5213112341720972308927 11421036014050568652027339573807169	22624395723923324778408332613592610809065898663506 26570060781491115767524167798198937581068019871	97	320.083

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 84199 skipped known factor: 193445668956521	-	-	0.114	-	-	7.840%

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	?	?	193445668956521	47.459	15	1.15675e-5	5.82624e-6	2.43513e-5

ECM factoring results:

Total ECM effort:	18.798 GHz-days
Estimated T-Level:	36.617

Digits	B1	Complete	FacMiss
20	11000	415.067	0.000%
25	50000	96.040	0.000%
30	250000	17.466	0.000%
35	1000000	2.600	7.424%
40	3000000	0.323	72.362%
45	11000000	0.035	96.551%
50	44000000	0.003	99.669%

ECM Summary

B1	B2	factor	curves	GHz-days
		2332966266085570691423	1	0.00000e+0
		5213112341720972308927	1	0.00000e+0
50000	5000000		148	0.030
250000	25000000		551	0.567
500000	50000000		10	0.021
1000000	100000000		489	2.012
1000000	100000000	11421036014050568652027339573807169	146	0.601
3000000	300000000		1,261	15.57

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29	ANONYMOUS	Manual testing			5213112341720972308927	72.143		1		1	-
2008-08-29	ANONYMOUS	Manual testing			2332966266085570691423	70.983		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	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
2010-04-09	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
2011-02-07	BloodIce	Mjolnir4	250000	25000000						200	0.206
2011-04-09	James Hintz	17_051310	250000	25000000						11	0.011
2012-09-15	BloodIce	Mjolnir4	250000	25000000						190	0.195
2012-09-16	BloodIce	Mjolnir4	1000000	100000000						100	0.412
2012-09-16	BloodIce	Mjolnir4	1000000	100000000						100	0.412
2017-05-01	kkmrkkblmbrbk	c4.large	1000000	100000000	11421036014050568652027339573807169	113.137	146	2		146	0.601
2017-05-01	kkmrkkblmbrbk	c4.large	1000000	100000000						289	1.189
2019-03-09	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-10	Niels_Mache_Nextcloud	SuperDry-X	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
2019-03-17	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-20	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-22	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-24	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-27	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-29	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-31	Niels_Mache_Nextcloud	SuperDry-X	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	SuperDry-JP	3000000	300000000						3	0.037
2019-04-09	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-11	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-13	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-17	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-24	Niels_Mache_Nextcloud	SuperDry-X	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	SuperDry-JP	3000000	300000000						3	0.037
2019-05-04	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-07	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-X	3000000	300000000						3	0.037
2019-05-14	Niels_Mache_Nextcloud	SuperDry-JP	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
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-28	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-01	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-05	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
2019-07-09	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-24	Niels_Mache_Nextcloud	SuperDry-Y	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	SuperDry3	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	SuperDry-Y	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	SuperDry3	3000000	300000000						3	0.037
2019-08-25	Niels_Mache_Nextcloud	SuperDry3	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	SuperDry3	3000000	300000000						3	0.037
2019-09-07	Niels_Mache_Nextcloud	SuperDry-Y	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	SuperDry3	3000000	300000000						3	0.037
2019-09-17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-20	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-25	Niels_Mache_Nextcloud	SuperDry-Y	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	SuperDry3	3000000	300000000						3	0.037
2019-10-10	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	SuperDry-Y	3000000	300000000						3	0.037
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-26	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-28	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-02	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-12	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2021-10-20	nordi	sweet16	3000000	300000000						1000	12.35

Lucas-Lehmer results:
No L-L results for M14033

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

84199

193445668956521

2332966266085570691423

5213112341720972308927

11421036014050568652027339573807169

48981F0FB65E112F

2017-09-21

Oliver Kruse

Manual testing

84199

193445668956521

2332966266085570691423

5213112341720972308927

11421036014050568652027339573807169

48981F0FB65E112F

2017-10-02

kkmrkkblmbrbk

Manual testing

84199

193445668956521

2332966266085570691423

5213112341720972308927

11421036014050568652027339573807169

48981F0FB65E11__

2017-12-07

ATH

Manual testing

84199

193445668956521

2332966266085570691423

5213112341720972308927

11421036014050568652027339573807169

48981F0FB65E11__

2020-04-17

Oliver Kruse

Manual testing

84199

193445668956521

2332966266085570691423

5213112341720972308927

11421036014050568652027339573807169

E4568895B87BA5__

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 = 400000000 (P-1 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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=36.62 ~= 105-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2023-03-25T13:08:14+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