M15 641 Mersenne number exponent details

is 2 ¹⁵⁶⁴¹ - 1

has 4709 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	unknown	400000000	400000000	0.1382	30.9138%	0.1382	30.9138%
Target	2⁴⁴	0.0001	68.1818%	500	10000	0.0000	1.4483%	0.0002	68.6426%
Difference	-44	-0.0001	-68.1818%	+399999500	+399990000	+0.1382	+29.4655%	+0.1381	-37.7289%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15641	594359	6	19.181	19 19	-	1	19	4.484e-12	6.845e-10	7.033e-10
15641	8760877180143839657	19	62.926	280061287006708 2² × 29 × 811 × 2976968483	2008-08-29	811	2976968483	97.530	0.0561	0.1047
15641	1503187649905798581024943	25	80.314	48052798731084923631 3³ × 17 × 104690193313910509	2008-08-29	27	104690193313910509	17,251,470	1,971,142	3,681,544
15641	5476635295941434870665009	25	82.180	175073054662151872344 2³ × 3² × 37 × 43 × 1972247 × 774917251	2008-08-29	1972247	774917251	124,755,547	0.0152	0.0273
15641	21236324132398144220838855087690902969	38	123.998	678867212211436104495839623032124 2² × 31 × 811 × 1879 × 3592655000101905849708229	2017-10-20	1879	3592655000101905849708229	1.120e+13	6.764e+13	1.263e+14

exponent	prime factors	composite factor	digits	bits*
15641	594359 8760877180143839657	5207106199913112394694863	25	82.107
15641	594359 1503187649905798581024943	893433108410360538819404096537	30	99.495
15641	594359 5476635295941434870665009	3255087477860455288293584084231	31	101.361
15641	594359 21236324132398144220838855087690902969	12622000375008028600953561071064877397751871	44	143.179
15641	8760877180143839657 1503187649905798581024943	13169242379533757934146890289706454509564551	44	143.240
15641	8760877180143839657 5476635295941434870665009	47980129188183620717347638256478914256461913	44	145.105
15641	594359 8760877180143839657 1503187649905798581024943	7827257731457304831981611565699638595850276967809	49	162.421
15641	1503187649905798581024943 5476635295941434870665009	8232410539897353204776424424412791888531226319487	49	162.494
15641	594359 8760877180143839657 5476635295941434870665009	28517421604159628625942024926482550998556446148767	50	164.286
15641	594359 1503187649905798581024943 5476635295941434870665009	48930072960828509534377108444695625740755311440239 73833	55	181.675
15641	8760877180143839657 21236324132398144220838855087690902969	18604882748166482595784097764724012388279251182508 1241633	57	186.924
15641	1503187649905798581024943 21236324132398144220838855087690902969	31922180165217363408597688182221369752053663919381 161181755767	62	204.312
15641	594359 8760877180143839657 21236324132398144220838855087690902969	11057979505317482429147640563343599279085267453584 3461695748247	63	206.105
15641	5476635295941434870665009 21236324132398144220838855087690902969	11630360229954454569533080464838695557103064087481 3368722511721	63	206.177
15641	594359 1503187649905798581024943 21236324132398144220838855087690902969	18973235080818426898170713350296911104460863633459 467578827175918353	68	223.493
15641	594359 5476635295941434870665009 21236324132398144220838855087690902969	69126092759154996634931121720010622526242200679713 199020543343981839	68	225.358
15641	8760877180143839657 1503187649905798581024943 5476635295941434870665009	72123137636562348342467663842015555007216282791467 761434244382495959	68	225.420
15641	594359 8760877180143839657 1503187649905798581024943 5476635295941434870665009	42867035962529560798480738213476523258534062623653 987218296056935915695281	74	244.601
15641	8760877180143839657 1503187649905798581024943 21236324132398144220838855087690902969	27966629974989310427180757107951592228823287768990 1348782902993320342524183051919	81	267.238
15641	8760877180143839657 5476635295941434870665009 21236324132398144220838855087690902969	10189215753546044050383217777041284123140741960135 38965319902023687487394127119697	82	269.103
15641	594359 8760877180143839657 1503187649905798581024943 21236324132398144220838855087690902969	16622218225304671556188727613925000405531180495089 2075761257440206885462330914555524921	87	286.419
15641	1503187649905798581024943 5476635295941434870665009 21236324132398144220838855087690902969	17482613861623099734555412970596490016646074611906 8326088497292568955298493713510856903	87	286.492
15641	594359 8760877180143839657 5476635295941434870665009 21236324132398144220838855087690902969	60560520860618731957417189347444805901458082506841 1005888571646896871320086000735989223	87	288.284
15641	594359 1503187649905798581024943 5476635295941434870665009 21236324132398144220838855087690902969	10390948892180443935130620697790759209803744260258 3331225633162313991702257425068599398010177	93	305.673
15641	8760877180143839657 1503187649905798581024943 5476635295941434870665009 21236324132398144220838855087690902969	15316303282956018540664988706867004202411636541343 02217515245460143277653222210249707592106231462703 602271	106	349.418
15641	594359 8760877180143839657 1503187649905798581024943 5476635295941434870665009 21236324132398144220838855087690902969	91033827029544562238111020228247657507411778830760 97317001437764452983626914996618059547366676259410 50342189289	111	368.598

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: 594359	-	-	0.138	-	-	30.914%

Trial Factoring results:
No TF results for M15641

ECM factoring results:

Total ECM effort:	20.808 GHz-days
Estimated T-Level:	36.447

Digits	B1	Complete	FacMiss
20	11000	468.726	0.000%
25	50000	101.792	0.000%
30	250000	17.416	0.000%
35	1000000	2.450	8.626%
40	3000000	0.289	74.876%
45	11000000	0.030	97.063%
50	44000000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
		8760877180143839657	1	0.00000e+0
		1503187649905798581024943	1	0.00000e+0
		5476635295941434870665009	1	0.00000e+0
50000	5000000		148	0.037
250000	25000000		572	0.711
1000000	100000000		956	4.754
1000000	100000000	21236324132398144220838855087690902969	465	2.312
3000000	300000000		871	12.99

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29	ANONYMOUS	Manual testing			8760877180143839657	62.926		1		1	-
2008-08-29	ANONYMOUS	Manual testing			5476635295941434870665009	82.180		1		1	-
2008-08-29	ANONYMOUS	Manual testing			1503187649905798581024943	80.314		1		1	-
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.012
2009-06-08	unconnected	dual5430	250000	25000000						30	0.037
2009-06-12	Rob_Dee	twopc	50000	5000000						80	0.020
2009-07-04	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-05	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-06	Rob_Dee	twopc	250000	25000000						10	0.012
2010-04-07	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-09	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-09	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-09	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-10	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-10	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-11	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-11	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-12	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-12	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-13	James Hintz	14_091909	250000	25000000						11	0.014
2010-04-13	James Hintz	14_091909	250000	25000000						11	0.014
2011-04-07	James Hintz	17_051310	250000	25000000						11	0.014
2014-08-18	James Hintz	08_04_2014	250000	25000000						389	0.484
2014-08-18	James Hintz	08_04_2014	1000000	100000000						11	0.055
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-02	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-03	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-03	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-06	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-06	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-07	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-07	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-07	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-08	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-08	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-08	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-09	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-09	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-09	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-10	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-10	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-11	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-11	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-11	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.015
2017-10-20	James Hintz	10_12_2017	1000000	100000000	21236324132398144220838855087690902969	123.998	465	2		465	2.312
2017-10-20	James Hintz	10_12_2017	1000000	100000000						828	4.118
2019-05-02	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-05	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-05-08	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-05-11	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-05-14	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-05-16	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-25	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-29	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-03	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-07	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-12	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-16	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-25	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-29	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-07-15	Niels_Mache_Nextcloud		3000000	300000000						3	0.045
2019-07-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-07-25	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-07-28	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-07-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-03	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-08-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-11	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-08-14	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-08-17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-29	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-08-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-12	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-18	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-09-21	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-09-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-26	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-09-29	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-10-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-19	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-25	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-10-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-08	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-11-12	Lin_yq		3000000	300000000						3	0.045
2021-11-30	nordi	sweet16_ccx0	3000000	300000000						700	10.44

Lucas-Lehmer results:
No L-L results for M15641

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

594359

8760877180143839657

1503187649905798581024943

5476635295941434870665009

5833C2B75D2AD094

2017-09-21

Oliver Kruse

Manual testing

594359

8760877180143839657

1503187649905798581024943

5476635295941434870665009

5833C2B75D2AD094

2017-10-02

kkmrkkblmbrbk

Manual testing

594359

8760877180143839657

1503187649905798581024943

5476635295941434870665009

5833C2B75D2AD0__

2017-10-20

alpertron

Manual testing

594359

8760877180143839657

1503187649905798581024943

5476635295941434870665009

21236324132398144220838855087690902969

2017-10-20

Oliver Kruse

GTX-0

594359

8760877180143839657

1503187649905798581024943

5476635295941434870665009

21236324132398144220838855087690902969

2CB00AA18CD881__

2017-10-21

kkmrkkblmbrbk

c4.xlarge

594359

8760877180143839657

1503187649905798581024943

5476635295941434870665009

21236324132398144220838855087690902969

BAB4026245E138__

2017-11-01

kkmrkkblmbrbk

c4.xlarge

594359

8760877180143839657

1503187649905798581024943

5476635295941434870665009

21236324132398144220838855087690902969

2CB00AA18CD881__

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

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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=36.45 ~= 104-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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