M17 837 Mersenne number exponent details

is 2 ¹⁷⁸³⁷ - 1

has 5370 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	1,665.8585	77.6119%	5900000000	16484172846891750	383,080.8196	35.7713%	384,746.6781	85.6204%
Target	2⁴⁴	0.0001	65.9091%	500	50000	0.0000	1.5068%	0.0001	66.4228%
Difference	+23	+1,665.8583	+11.7028%	+5899999500	+16484172846841750	+383,080.8196	+34.2645%	+384,746.6780	+19.1977%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
17837	354135799	9	28.400	9927 3² × 1103	-	9	1103	2.303e-9	2.926e-8	4.781e-8
17837	12814508197081	14	43.543	359211420 2² × 3² × 5 × 79 × 25261	2008-08-26	79	25261	9.129e-5	6.189e-7	1.096e-6
17837	4834713964766767	16	52.102	135524863059 3 × 193 × 234067121	2008-08-29	193	234067121	0.0654	0.0054	0.0102
17837	27818292235191449986888865929	29	94.490	779791787721910915145172 2² × 3² × 11 × 313 × 6291281728804909439	2009-05-31	313	6291281728804909439	2.313e+11	146,204,145	273,068,627
17837	102367402667345090561243144476554967687	39	126.267	2869524097868057704805829020478639 3 × 71 × 14767 × 258763 × 4363291 × 808019128560373	2023-04-13	4363291	808019128560373	7.742e+12	18,778	35,071

exponent	prime factors	composite factor	digits	bits*
17837	354135799 12814508197081	4538076099165329402719	22	71.943
17837	354135799 4834713964766767	1712145292849136880191833	25	80.502
17837	12814508197081 4834713964766767	61954481732045716745835207127	29	95.645
17837	354135799 27818292235191449986888865929	9851453147525020059075428059970292271	37	122.890
17837	354135799 12814508197081 4834713964766767	21940299889808913804314030998250639473	38	124.045
17837	12814508197081 27818292235191449986888865929	356477733876655569392353422424142518153249	42	138.033
17837	4834713964766767 27818292235191449986888865929	134493485945443023947320259555156947617781543	45	146.592
17837	354135799 102367402667345090561243144476554967687	36251961935154984854633199402477230249254926913	47	154.667
17837	354135799 12814508197081 27818292235191449986888865929	12624152711211878751456102374055822755607283906095 1	51	166.433
17837	12814508197081 102367402667345090561243144476554967687	13117879205945850868408125577403296024487325827216 47	52	169.810
17837	354135799 4834713964766767 27818292235191449986888865929	47628958105584735694560394026452890215024213337757 857	53	174.992
17837	4834713964766767 102367402667345090561243144476554967687	49491711121271610238431902085444249505076230417645 7929	54	178.369
17837	12814508197081 4834713964766767 27818292235191449986888865929	17234678781018778975309836471934592198935289184858 48275983	58	190.135
17837	354135799 12814508197081 102367402667345090561243144476554967687	46455106337831194480185554094460525828653426971946 4054940953	60	198.210
17837	354135799 4834713964766767 102367402667345090561243144476554967687	17526786661808707587803662152118565568435525414861 0965676300271	63	206.769
17837	354135799 12814508197081 4834713964766767 27818292235191449986888865929	61034167406244313264257502115478978841091155847759 1749408012215417	66	218.535
17837	27818292235191449986888865929 102367402667345090561243144476554967687	28476863227577224587237124346554777011958889553469 40852454670236223	67	220.757
17837	12814508197081 4834713964766767 102367402667345090561243144476554967687	63421193785109993906459773412953971373823353200669 39212234437105249	67	221.912
17837	354135799 27818292235191449986888865929 102367402667345090561243144476554967687	10084676712111779263403664232929528854396893907170 64220989775755386350847177	76	249.157
17837	354135799 12814508197081 4834713964766767 102367402667345090561243144476554967687	22459715134623761994949263118955411602692060870578 26251409072959582601708951	76	250.312
17837	12814508197081 27818292235191449986888865929 102367402667345090561243144476554967687	36491699725694284684509382671320066580132529414792 007538037641522060388109065063	80	264.300
17837	4834713964766767 27818292235191449986888865929 102367402667345090561243144476554967687	13767748831912083658669916702257480383445860502322 095590669165664696626850990001041	83	272.859
17837	354135799 12814508197081 27818292235191449986888865929 102367402667345090561243144476554967687	12923017239226826336482193155304686163088430830198 370008296983072490431669253855228490337	89	292.700
17837	354135799 4834713964766767 27818292235191449986888865929 102367402667345090561243144476554967687	48756527330205024442179142286173979193184261822323 76677356001927330706042480197959665366759	91	301.259
17837	12814508197081 4834713964766767 27818292235191449986888865929 102367402667345090561243144476554967687	17642693026188975888276027647473795403111653842378 4146181535669868250080719102092679863223161321	96	316.402
17837	354135799 12814508197081 4834713964766767 27818292235191449986888865929 102367402667345090561243144476554967687	62479091913411609011863657834842228666434726196820 99921153093349579296706727371415375541374494971823 0479	104	344.802

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: 354135799 skipped known factor: 12814508197081	-	-	2.13271e-5	-	-	0.218%
2023-04-13	JacobZ	GreatLakes	5900000000	16484172846891750			102367402667345090561243144476554967687	39	126.267	383,081	1.04941e-5	766,162	35.771%

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	?	?	12814508197081	43.543	14	2.55954e-5	1.09281e-5	5.33081e-5
2008-08-29	ANONYMOUS	Manual testing	?	?	4834713964766767	52.102	16	0.032	1.09281e-5	0.066

ECM factoring results:

Total ECM effort:	21.827 GHz-days
Estimated T-Level:	36.169

Digits	B1	Complete	FacMiss
20	11000	557.737	0.000%
25	50000	111.879	0.000%
30	250000	17.465	0.000%
35	1000000	2.218	10.882%
40	3000000	0.234	79.152%
45	11000000	0.021	97.919%
50	44000000	0.002	99.834%

ECM Summary

B1	B2	factor	curves	GHz-days
		27818292235191449986888865929	1	0.00000e+0
50000	5000000		68	0.021
250000	25000000		467	0.717
1000000	100000000		2,836	17.41
3000000	300000000		200	3.683

ECM Details

										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						5	0.031
2009-05-31	Matthias Wurtinger	WUR_E6600			27818292235191449986888865929	94.490		1		1	-
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
2009-07-03	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
2017-10-03	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-03	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-04	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-05	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-06	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-07	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-07	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-08	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-08	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-08	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-09	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-09	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-10	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-10	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-10	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-11	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-11	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-10-12	Oliver Kruse	ECM-HTC	1000000	100000000						3	0.018
2017-11-17	kkmrkkblmbrbk	c4.large	1000000	100000000						1410	8.654
2017-11-18	James Hintz	10_12_2017	1000000	100000000						1329	8.157
2022-02-28	nordi	sweet16_ccx3	3000000	300000000						200	3.683

Lucas-Lehmer results:
No L-L results for M17837

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

354135799

12814508197081

4834713964766767

27818292235191449986888865929

7C123A743157BE9D

2017-09-21

Oliver Kruse

Manual testing

354135799

12814508197081

4834713964766767

27818292235191449986888865929

7C123A743157BE9D

2017-10-02

kkmrkkblmbrbk

Manual testing

354135799

12814508197081

4834713964766767

27818292235191449986888865929

7C123A743157BE__

2017-12-07

ATH

Manual testing

354135799

12814508197081

4834713964766767

27818292235191449986888865929

7C123A743157BE__

2020-04-17

Oliver Kruse

Manual testing

354135799

12814508197081

4834713964766767

27818292235191449986888865929

D07052171F571B__

2023-04-13

JacobZ

GreatLakes

354135799

12814508197081

4834713964766767

27818292235191449986888865929

102367402667345090561243144476554967687

D07052171F571B5C

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 = 5900000000, B2 = 16484172846891750 (P-1 stage 2)

B1 = 5900000000 (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

10¹⁸

10¹⁹

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=36.17 ~= 104-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

Last modified: 2023-09-25T11:53:03+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