M1684877 Mersenne number exponent details

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M1684877

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is 2 ^1684877 - 1

has 507199 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	F2854F927EB0DAA0	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	2⁷⁰	141.8208	70.0000%	10000000	10000000	0.6824	4.1182%	142.5032	71.2355%	1.2355%
PrimeNet	2⁵⁷	0.0114	63.1579%	8000	130000	0.0010	2.7267%	0.0124	64.1625%	1.0046%
GPU72	2⁶¹	0.1823	65.5738%	7000	90000	0.0008	1.2562%	0.1831	66.0062%	0.4325%
Difference	+9	+141.6385	+4.4262%	+9993000	+9910000	+0.6816	+2.8620%	+142.3201	+5.2292%	+5.2292%

Known prime factors (1 factor, 67.3 bits, 0.00399586% 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
1684877	184910898823017897191	21	67.325	54873708532735 5 × 307 × 479 × 74631199	2014-02-07	479	74631199	23.607	0.2775	0.5182

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2008-10-04T00:00:00	Richard B. Woods	v4_computers	1000000	1000000		-		-	-	0.068	-	-	1.868%
2008-10-14T00:00:00	Richard B. Woods	v4_computers	2000000	2000000		-		-	-	0.136	-	-	2.446%
2008-10-14T00:00:00	Richard B. Woods	v4_computers	3000000	3000000		-		-	-	0.205	-	-	2.824%
2008-10-14T00:00:00	Richard B. Woods	v4_computers	4000000	4000000		-		-	-	0.273	-	-	3.111%
2008-11-12T08:49:00	Richard B. Woods	Manual testing	5000000	5000000		-		-	-	0.341	-	-	3.343%
2008-11-12T08:50:00	Richard B. Woods	Manual testing	6000000	6000000		-		-	-	0.409	-	-	3.539%
2008-11-12T08:52:00	Richard B. Woods	Manual testing	8000000	8000000		-		-	-	0.546	-	-	3.860%
2008-11-26T02:14:00	Richard B. Woods	Manual testing	10000000	10000000		-		-	-	0.682	-	-	4.118%
2016-03-17T19:18:42	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	3.735%

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	-	-
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2022-03-08T23:06:22	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.068	-	-
2008-10-04T00:00:00	Richard B. Woods	v4_computers	2¹	2⁶¹		-	-	0.182	-	-
2008-10-14T00:00:00	Richard B. Woods	v4_computers	2¹	2⁶²		-	-	0.365	-	-
2008-10-14T00:00:00	Richard B. Woods	v4_computers	2¹	2⁶³		-	-	0.947	-	-
2008-10-14T00:00:00	Richard B. Woods	v4_computers	2¹	2⁶⁴		-	-	2.113	-	-
2008-11-26T02:14:00	Richard B. Woods	Manual testing	2¹	2⁶⁵		-	-	4.330	-	-
2014-01-18T11:19:00	Never Odd Or Even	Manual testing	2⁶⁵	2⁶⁶		-	-	4.435	-	-
2014-01-18T11:19:00	Never Odd Or Even	Manual testing	2⁶⁶	2⁶⁷		-	-	8.870	-	-
2014-01-18T11:19:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸	MISSED FACTOR!	-	-	17.74	-	-
2014-02-07T18:53:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸	184910898823017897191	67.325	21	5.971	0.161	12.14
2014-01-18T11:19:00	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	35.48	-	-
2014-01-18T11:19:00	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰		-	-	70.96	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.906 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:	14.906 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		251	14.91

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-12T09:38:00	Team_Bundu	bundu4	50000	5000000						3	0.178
2009-09-21T15:53:00	Piepen	T41-2000	50000	5000000						3	0.178
2010-06-12T22:22:00	Lupo	yorick	50000	5000000						3	0.178
2011-11-02T17:21:00	Bud	annan	50000	5000000						3	0.178
2013-04-05T18:16:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2013-12-25T00:53:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-01-27T11:16:15	TJAOI	Manual testing	50000	5000000						233	13.84

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	F2854F927EB0DAA0	0.079

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T00:42:15

Oliver Kruse

GTX-3

184910898823017897191

0A3F5DC16B3914__

2017-11-03T05:17:50

ATH

ec2-1xf

184910898823017897191

0A3F5DC16B3914__

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 = 10000000 (P-1 stage 1)

B1 = 8000000 (P-1 stage 1)

B1 = 6000000 (P-1 stage 1)

B1 = 5000000 (P-1 stage 1)

B1 = 4000000 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-08T23:06:22+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