M17 027 Mersenne number exponent details

is 2 ¹⁷⁰²⁷ - 1

has 5126 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	1,745.1059	77.6119%	400000000	400000000	0.1706	7.9661%	1,745.2765	79.3954%
Target	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.4859%	0.0001	66.4156%
Difference	+23	+1,745.1057	+11.7028%	+399999500	+399990000	+0.1706	+6.4802%	+1,745.2763	+12.9798%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
17027	442703	6	18.756	13 13	-	1	13	2.057e-12	7.054e-10	8.681e-10
17027	96032281	8	26.517	2820 2² × 3 × 5 × 47	2008-08-26	5	47	8.455e-10	3.109e-9	4.340e-9
17027	547725625729	12	38.995	16084032 2⁶ × 3 × 19 × 4409	2008-08-26	64	4409	2.994e-6	1.283e-7	1.912e-7
17027	350622873550009	15	48.317	10296084852 2² × 3³ × 79 × 1206761	2008-08-26	79	1206761	0.0040	2.808e-5	5.238e-5
17027	571308013771680925760863	24	78.919	16776531795726814053 3 × 1193 × 4687491420991007	2008-08-29	1193	4687491420991007	4,928,313	108,933	203,457

exponent	prime factors	composite factor	digits	bits*
17027	442703 96032281	42513778895543	14	45.273
17027	442703 547725625729	242479777687105487	18	57.751
17027	96032281 547725625729	52599341200908157849	20	65.512
17027	442703 350622873550009	155221797989209634327	21	67.073
17027	96032281 350622873550009	33671114317781931840529	23	74.834
17027	442703 96032281 547725625729	23285886147665644204225847	26	84.268
17027	547725625729 350622873550009	192045132810078723098581561	27	87.312
17027	442703 96032281 350622873550009	14906303321825014571597709887	29	93.590
17027	442703 571308013771680925760863	252919771620764460877111332689	30	97.675
17027	96032281 571308013771680925760863	54864011716073932505007334418503	32	105.436
17027	442703 547725625729 350622873550009	85018956430420280951911352799383	32	106.068
17027	96032281 547725625729 350622873550009	18442532158699799568724175167370641	35	113.829
17027	547725625729 571308013771680925760863	312920039327086084402502682094044127	36	117.913
17027	442703 96032281 571308013771680925760863	24288462578741078141764261969074533609	38	124.192
17027	350622873550009 571308013771680925760863	200313657470774881576121950316205497767	39	127.236
17027	442703 96032281 547725625729 350622873550009	8164564314252877368472898519120484882623	40	132.585
17027	442703 547725625729 571308013771680925760863	138530640170218990823241144871079617155281	42	136.669
17027	96032281 547725625729 571308013771680925760863	30050425147189781768530854670108914030463687	44	144.430
17027	442703 350622873550009 571308013771680925760863	88679457103284452398393915770835122477944201	44	145.992
17027	96032281 350622873550009 571308013771680925760863	19236577442371202715259866023033885215305416527	47	153.753
17027	442703 96032281 547725625729 571308013771680925760863	13303413363936357958273914955021226568028365625961	50	163.186
17027	547725625729 350622873550009 571308013771680925760863	10971692338024474754177726898215550567337998724714 3	51	166.230
17027	442703 96032281 350622873550009 571308013771680925760863	85160905434700585556536884679951700864713538127524 81	52	172.509
17027	442703 547725625729 350622873550009 571308013771680925760863	48572011131204490470987422310207188828122340494271 947529	56	184.986
17027	96032281 547725625729 350622873550009 571308013771680925760863	10536366416507133444706013934306941506523121155094 053023183	59	192.747
17027	442703 96032281 547725625729 350622873550009 571308013771680925760863	46644810216869574973716864867594859257623053047236 02555522183649	64	211.503

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: 442703 skipped known factor: 96032281 skipped known factor: 547725625729 skipped known factor: 350622873550009	-	-	0.171	-	-	7.966%

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	?	?	350622873550009	48.317	15	0.002	1.04516e-5	0.004
2008-08-26	ANONYMOUS	Manual testing	?	?	547725625729	38.995	12	8.43493e-7	0.000	2.42148e-5
2008-08-26	ANONYMOUS	Manual testing	?	?	96032281	26.517	8	3.20489e-10	0.000	9.47565e-9

ECM factoring results:

Total ECM effort:	38.756 GHz-days
Estimated T-Level:	37.160

Digits	B1	Complete	FacMiss
20	11000	603.503	0.000%
25	50000	133.626	0.000%
30	250000	24.007	0.000%
35	1000000	3.512	2.983%
40	3000000	0.432	64.924%
45	11000000	0.046	95.518%
50	44000000	0.004	99.571%

ECM Summary

B1	B2	factor	curves	GHz-days
		571308013771680925760863	1	0.00000e+0
50000	5000000		68	0.021
250000	25000000		467	0.717
1000000	100000000		1,451	8.906
3000000	300000000		708	13.04
3000000	528000000		700	16.08

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29	ANONYMOUS	Manual testing			571308013771680925760863	78.919		1		1	-
2009-04-07	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
2014-08-27	James Hintz	08_04_2014	250000	25000000						450	0.691
2014-08-27	James Hintz	08_04_2014	1000000	100000000						11	0.068
2017-09-25	kkmrkkblmbrbk	c4.large	1000000	100000000						1410	8.654
2019-07-23	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-07-26	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-07-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-08-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-11	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-08-14	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-08-17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-20	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-08-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-02	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-09-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-08	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-09-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-24	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-30	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-04	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-13	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-19	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-22	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	SuperDry-Y	3000000	300000000						3	0.055
2019-11-01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2022-01-14	nordi	sweet16_ccx3	3000000	300000000						600	11.05
2022-01-29	fbaur	Manual testing	3000000	528000000						350	8.038
2022-01-29	fbaur	Manual testing	3000000	528000000						350	8.038

Lucas-Lehmer results:
No L-L results for M17027

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

9BA4799ECE4164__

2017-09-21

Oliver Kruse

Manual testing

9BA4799ECE4164__

2017-10-02

kkmrkkblmbrbk

Manual testing

442703

96032281

547725625729

350622873550009

571308013771680925760863

9BA4799ECE4164__

2017-12-07

ATH

Manual testing

442703

96032281

547725625729

350622873550009

571308013771680925760863

9BA4799ECE4164__

2020-04-17

Oliver Kruse

Manual testing

442703

96032281

547725625729

350622873550009

571308013771680925760863

2E1001433D8A50__

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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=37.16 ~= 107-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