M1837709 Mersenne number exponent details

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M1837709

<<<

>>>

is 2 ^1837709 - 1

has 553206 decimal digits

takes 0.100 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	F3FE90F66CDB5636	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	16.1690	68.6567%	2780000	91760000	0.6000	8.1327%	16.7690	71.2058%	2.5490%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8814%	0.0117	64.2195%	1.0616%
GPU72	2⁶¹	0.1672	65.5738%	9000	140000	0.0013	1.5960%	0.1684	66.1232%	0.5494%
Difference	+6	+16.0018	+3.0829%	+2771000	+91620000	+0.5988	+6.5367%	+16.6006	+5.0826%	+5.0826%

Known prime factors (3 factors, 240.7 bits, 0.01309731% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1837709	210029643795242038560503	24	77.475	57144423789414439 17 × 89 × 157 × 1093 × 220097503	2021-04-23	1093	220097503	27,540	0.9434	1.7618
1837709	2062332678107628333913817	25	80.771	561115137953731612 2² × 19 × 7383093920443837	2021-04-23	19	7383093920443837	169,355	31,642,095	59,098,621
1837709	6582739347335789939763719	25	82.445	1791017878057894351 194479 × 9209312460769	2016-09-08	194479	9209312460769	854,964	39,469	73,717

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1837709	210029643795242038560503 2062332678107628333913817	433150997770232737676855769962859351482742169951	48	158.245
1837709	210029643795242038560503 6582739347335789939763719	1382570400317860020059314020359666404626705790657	49	159.920
1837709	2062332678107628333913817 6582739347335789939763719	13575798467475481100261047477128771045235489405423	50	163.216
1837709	210029643795242038560503 2062332678107628333913817 6582739347335789939763719	28513201163598680551028290820448937585258068592728 43295852622290281807769	73	240.690

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-08T05:49:00	Carsten Kossendey	leela	100000	1675000		-		-	-	0.015	-	-	2.493%
2014-05-19T21:00:00	Jocelyn Larouche	Manual testing	134926	134926		-		-	-	0.011	-	-	1.061%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	169852	169852		-		-	-	0.013	-	-	1.200%
2015-07-03T09:57:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	8.133%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-16T14:26:00	Architects Cubed	a3_lm	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.167	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.868	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.534	-	-
2015-04-26T21:13:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.068	-	-
2015-04-26T21:13:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.033	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.066	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.238 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.238 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.575	0.019%
25	50000	0.777	45.986%
30	250000	0.048	95.308%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.280
50000	5000000	6582739347335789939763719	3	0.207
50000	6600000		108	8.414
50000	6600000	210029643795242038560503	7	0.545
50000	6600000	2062332678107628333913817	100	7.791

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-07T15:41:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-19T00:04:00	SubPrime	abd1	50000	5000000						3	0.207
2010-11-17T02:16:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.207
2012-06-03T23:17:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.207
2013-08-27T05:22:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-13T00:18:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-11-13T15:19:00	mikr	MSI	50000	5000000						12	0.829
2016-06-01T19:21:40	Bruce	DESK3	50000	5000000						3	0.207
2016-09-08T04:38:11	Bruce	DESK3	50000	5000000	6582739347335789939763719	82.445	3	2		3	0.207
2021-04-23T12:19:04	TJAOI	Manual testing	50000	6600000	210029643795242038560503	77.475	7	2		7	0.545
2021-04-23T12:19:04	TJAOI	Manual testing	50000	6600000	2062332678107628333913817	80.771	100	2		100	7.791
2021-04-23T12:19:04	TJAOI	Manual testing	50000	6600000						108	8.414

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	F3FE90F66CDB5636	0.100
2015-07-10T01:00:00	MadPoo	Manual testing	F3FE90F66CDB5636	0.100

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T03:29:14

Oliver Kruse

GTX-2

6582739347335789939763719

9F3BB3D869A1D3__

2017-11-06T10:38:21

kkmrkkblmbrbk

c4.xlarge

6582739347335789939763719

9F3BB3D869A1D3__

2021-04-23T12:52:34

ATH

ec2-PRPCFDC

210029643795242038560503

2062332678107628333913817

6582739347335789939763719

E76FDE7E265D456F

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 = 2780000, B2 = 91760000 (P-1 stage 2)

B1 = 2780000 (P-1 stage 1)

B1 = 100000, B2 = 1675000 (P-1 stage 2)

B1 = 169852 (P-1 stage 1)

B1 = 134926 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-04-23T12:52:34+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