M17 657 Mersenne number exponent details

is 2 ¹⁷⁶⁵⁷ - 1

has 5316 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	1,682.8407	77.6119%	400000000	400000000	0.1706	7.9900%	1,683.0113	79.4007%
Target	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.5022%	0.0001	66.4212%
Difference	+23	+1,682.8405	+11.7028%	+399999500	+399990000	+0.1706	+6.4878%	+1,683.0111	+12.9795%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
17657	105943	6	16.693	3 3	-	1	3	4.948e-13	4.730e-10	8.681e-10
17657	423769	6	18.693	12 2² × 3	2008-08-26	4	4	1.983e-12	1.706e-9	3.472e-9
17657	55513609	8	25.726	1572 2² × 3 × 131	2008-08-26	4	131	3.393e-10	4.658e-9	5.867e-9
17657	18278491087	11	34.089	517599 3² × 17² × 199	2008-08-26	289	289	1.341e-7	1.233e-7	2.509e-7
17657	27003468454621372923087713952503	32	104.413	764667510183535507818081043 7 × 11 × 71 × 131 × 1067707438501286005859	2017-11-13	131	1067707438501286005859	1.085e+13	2.481e+10	4.634e+10

exponent	prime factors	composite factor	digits	bits*
17657	105943 423769	44895359167	11	35.386
17657	105943 55513609	5881278278287	13	42.419
17657	423769 55513609	23524946572321	14	44.419
17657	105943 18278491087	1936478181230041	16	50.782
17657	423769 18278491087	7745857889446903	16	52.782
17657	55513609 18278491087	1014705007313702983	19	59.816
17657	105943 423769 55513609	2492303414711403703	19	61.112
17657	105943 423769 18278491087	820619422381673244529	21	69.475
17657	105943 55513609 18278491087	107500892589835635127969	24	76.509
17657	423769 55513609 18278491087	430000526244320599402927	24	78.509
17657	105943 423769 55513609 18278491087	45555545751902057262544295161	29	95.202
17657	105943 27003468454621372923087713952503	2860828458487952111590681679270025329	37	121.106
17657	423769 27003468454621372923087713952503	11443232823546444582243957453938243807	38	123.106
17657	55513609 27003468454621372923087713952503	1499059989433685139495478425063096113327	40	130.139
17657	18278491087 27003468454621372923087713952503	493582657465882428934361916000031626840761	42	138.502
17657	105943 423769 27003468454621372923087713952503	1212330415024980978376671584542579363645001	43	139.799
17657	105943 55513609 27003468454621372923087713952503	158814912460572904733569470786459591534202361	45	146.832
17657	423769 55513609 27003468454621372923087713952503	635255152662323317878859396710563176848469463	45	148.832
17657	105943 18278491087 27003468454621372923087713952503	52291627479907982168593104466791350642390742623	47	155.195
17657	423769 18278491087 27003468454621372923087713952503	209165029171659531027085614781417402474682448209	48	157.195
17657	55513609 18278491087 27003468454621372923087713952503	27400554655741927999832454069316599720071911416449	50	164.229
17657	105943 423769 55513609 27003468454621372923087713952503	67300836638504519266040001065707194644857400318609	50	165.525
17657	105943 423769 18278491087 27003468454621372923087713952503	22159570685533125695602531286787703870375282610606 087	53	173.888
17657	105943 55513609 18278491087 27003468454621372923087713952503	29028969618932670780862496814656085241435785111928 56407	55	180.922
17657	423769 55513609 18278491087 27003468454621372923087713952503	11611505645909101086560999228500226146775153829037 176281	56	182.922
17657	105943 423769 55513609 18278491087 27003468454621372923087713952503	12301577426445478964135319412649994586678001221096 85566737983	61	199.615

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: 105943 skipped known factor: 423769 skipped known factor: 55513609 skipped known factor: 18278491087	-	-	0.171	-	-	7.990%

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	?	?	18278491087	34.089	11	4.46089e-9	0.000	1.23065e-7
2008-08-26	ANONYMOUS	Manual testing	?	?	423769	18.693	6	5.13719e-15	0.000	1.41979e-13
2008-08-26	ANONYMOUS	Manual testing	?	?	55513609	25.726	8	8.61405e-11	0.000	2.38069e-9

ECM factoring results:

Total ECM effort:	22.238 GHz-days
Estimated T-Level:	36.246

Digits	B1	Complete	FacMiss
20	11000	423.703	0.000%
25	50000	91.186	0.000%
30	250000	15.421	0.000%
35	1000000	2.141	11.751%
40	3000000	0.249	77.935%
45	11000000	0.025	97.503%
50	44000000	0.002	99.775%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		68	0.021
250000	25000000		467	0.717
1000000	100000000		336	2.062
1000000	100000000	27003468454621372923087713952503	1,115	6.844
3000000	300000000		684	12.59

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-06	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.015
2009-05-31	Matthias Wurtinger	WUR_E6600	1000000	100000000						30	0.184
2009-06-30	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-30	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-30	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-01	Rob_Dee	twopc	50000	5000000						6	0.002
2009-07-02	Rob_Dee	twopc	250000	25000000						6	0.009
2011-04-05	James Hintz	17_051310	250000	25000000						11	0.017
2014-09-03	James Hintz	08_04_2014	1000000	100000000						11	0.068
2014-09-03	James Hintz	08_04_2014	250000	25000000						450	0.691
2017-10-13	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-13	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-13	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-11-13	James Hintz	10_12_2017	1000000	100000000	27003468454621372923087713952503	104.413	1115	2		1115	6.844
2017-11-13	James Hintz	10_12_2017	1000000	100000000						286	1.755
2019-08-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-21	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-08-24	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-31	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-09-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-19	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-26	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-29	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-11-01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2020-08-26	James Hintz	work_lappy_5_16_2019	3000000	300000000						100	1.841
2022-02-26	nordi	sweet16_ccx3	3000000	300000000						500	9.207

Lucas-Lehmer results:
No L-L results for M17657

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

105943

423769

55513609

18278491087

CF77C704E4CB84__

2017-09-21

Oliver Kruse

Manual testing

105943

423769

55513609

18278491087

CF77C704E4CB84__

2017-10-12

kkmrkkblmbrbk

Manual testing

105943

423769

55513609

18278491087

CF77C704E4CB84__

2017-11-14

Oliver Kruse

GTX-1

105943

423769

55513609

18278491087

27003468454621372923087713952503

2CD01821D1ED47__

2017-11-14

kkmrkkblmbrbk

c4.xlarge

105943

423769

55513609

18278491087

27003468454621372923087713952503

2CD01821D1ED47__

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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=36.25 ~= 104-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

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