M1677521 Mersenne number exponent details

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is 2 ^1677521 - 1

has 504985 decimal digits

takes 0.079 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	7FA340FDB48AA346	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	17.7130	68.6567%	1000000	20000000	0.1389	5.6985%	17.8519	70.4428%	1.7861%
PrimeNet	2⁵⁷	0.0114	63.1579%	7000	120000	0.0009	2.5717%	0.0123	64.1054%	0.9475%
GPU72	2⁶¹	0.1831	65.5738%	7000	90000	0.0008	1.2550%	0.1839	66.0058%	0.4321%
Difference	+6	+17.5299	+3.0829%	+993000	+19910000	+0.1381	+4.4435%	+17.6680	+4.4370%	+4.4370%

Known prime factors (1 factor, 74.1 bits, 0.00441703% 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
1677521	20197829620971818665231	23	74.097	6020142108793815 3 × 5 × 337 × 1367 × 871198399	2018-01-05	1367	871198399	3,384.0	3.2391	6.0497

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	markr	v4_computers	20000	320000		-		-	-	0.002	-	-	1.039%
2011-01-24T01:10:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.569%
2012-02-29T17:09:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.881%
2012-02-29T17:14:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.285%
2012-02-29T18:09:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.567%
2012-02-29T18:13:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.787%
2012-02-29T19:11:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.969%
2012-02-29T19:13:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	2.126%
2012-02-29T20:10:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.263%
2012-02-29T20:13:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.387%
2012-02-29T21:11:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.498%
2012-02-29T21:14:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.600%
2012-03-01T06:09:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.732%
2012-03-01T07:10:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.698%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:45	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.069	-	-
2010-04-26T15:50:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.092	-	-
2016-02-23T16:28:45	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.183	-	-
2010-08-31T00:27:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.951	-	-
2016-02-23T16:28:45	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.585	-	-
2015-05-13T07:35:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.170	-	-
2015-05-14T02:07:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.227	-	-
2015-10-13T10:54:04	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.455	-	-
2017-09-22T15:53:15	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.909	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.899 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:	14.899 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		249	14.78
50000	5000000	20197829620971818665231	2	0.119

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2015-06-27T00:55:00	MadPoo	Manual testing	7FA340FDB48AA346	0.079

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-07T09:05:21

AdolfNor

Manual testing

20197829620971818665231

9AE835F851BA53__

no

2018-01-10T04:45:05

alan145

Bear1

20197829620971818665231

9AE835F851BA53__

no

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 320000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-01-06T12:25:19+00:00