M1786271 Mersenne number exponent details

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M1786271

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is 2 ^1786271 - 1

has 537722 decimal digits

takes 0.097 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	16.6346	68.6567%	500000	15000000	0.1015	5.0538%	16.7361	70.2408%	1.5840%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8134%	0.0119	64.1944%	1.0365%
GPU72	2⁶¹	0.1720	65.5738%	8000	130000	0.0012	1.4927%	0.1731	66.0877%	0.5139%
Difference	+6	+16.4626	+3.0829%	+492000	+14870000	+0.1003	+3.5611%	+16.5630	+4.1531%	+4.1531%

Known prime factors (4 factors, 191.3 bits, 0.01070794% 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
1786271	117893887	9	26.813	33 3 × 11	-	3	11	5.041e-12	2.703e-7	4.803e-7
1786271	10235332831	11	33.253	2865 3 × 5 × 191	2008-07-15	5	191	1.038e-9	1.190e-6	1.562e-6
1786271	19693570114627063	17	54.129	5512481061 3 × 233 × 1499 × 5261	2014-11-05	1499	5261	0.0023	0.0001	0.0002
1786271	159568915180724164779193	24	77.079	44665371374423076 2² × 3² × 343627 × 3610614883	2020-06-01	343627	3610614883	20,162	15.500	28.901

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1786271	117893887 10235332831	1206683172185304097	19	60.066
1786271	117893887 19693570114627063	2321751529720420012463881	25	80.941
1786271	10235332831 19693570114627063	201570244753842811245005353	27	87.381
1786271	117893887 159568915180724164779193	18812199655028879260647559493191	32	103.891
1786271	10235332831 159568915180724164779193	1633240956356320342119527978585383	34	110.331
1786271	117893887 10235332831 19693570114627063	23763899657571887204680990400977111	35	114.194
1786271	19693570114627063 159568915180724164779193	3142481619226570083033097110776937100159	40	131.207
1786271	117893887 10235332831 159568915180724164779193	192549124752443962149640972000683563253721	42	137.144
1786271	117893887 19693570114627063 159568915180724164779193	370479372916674280766684568037962704692252828033	48	158.020
1786271	10235332831 19693570114627063 159568915180724164779193	32164345288083753598391054917546428218879348020129	50	164.460
1786271	117893887 10235332831 19693570114627063 159568915180724164779193	37919796888223284932645584102600129256901731221187 62051423	58	191.273

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:33:57	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 117893887 skipped known factor: 10235332831 skipped known factor: 19693570114627063	-	-	0.101	-	-	5.054%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	10235332831	33.253	11	3.97273e-10	0.208	8.51124e-10
2014-11-05T12:06:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	19693570114627063	54.129	17	0.001	0.205	0.002

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.290 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:	17.290 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		210	14.47
50000	5000000	159568915180724164779193	41	2.824

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-13T04:02:40	ATH	ec2-1xe	50000	5000000						3	0.207
2018-12-08T06:42:38	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-03-12T12:40:55	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-04-01T05:58:41	Hans Loeblich	crow	50000	5000000						3	0.207
2020-05-01T17:09:49	Greg	azure3	50000	5000000						3	0.207
2020-06-01T15:53:52	nordi	sweet16	50000	5000000	159568915180724164779193	77.079	41	2	4464118520648955	41	2.824
2020-11-06T10:16:11	TJAOI	Manual testing	50000	5000000						195	13.43

Lucas-Lehmer results:
No L-L results for M1786271

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T01:28:05

alpertron

Manual testing

117893887

10235332831

19693570114627063

A14C9BC2B8A99B__

2017-10-19T17:47:25

Oliver Kruse

Threadripper

117893887

10235332831

19693570114627063

A14C9BC2B8A99B__

2020-06-02T09:11:53

Klaus Nordmann

no1

117893887

10235332831

19693570114627063

159568915180724164779193

FD4957BF49F28491

2020-06-02T12:55:56

oodaira

com1

117893887

10235332831

19693570114627063

159568915180724164779193

FD4957BF49F28491

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁵⁵

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-11-06T10:16:11+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