M1681073 Mersenne number exponent details

≡

is 2^1681073-1

has 506054 decimal digits

takes 0.079 GHz-days to do one L-L test

Last-known PrimeNet details:
0 L-L tests remaining

	Residue	Status
L-L	8F8E552F74850236	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	2⁶³	0.9494	66.6667%	1000000	40000000	0.2132	9.1292%	1.1626	75.7959%	12.6380%
PrimeNet	2⁵⁷	0.0114	63.1579%	8000	130000	0.0010	2.7255%	0.0124	65.8834%	2.7255%
GPU72	2⁶¹	0.1827	65.5738%	7000	90000	0.0008	1.2556%	0.1835	66.8294%	1.2556%
Difference	+2	+0.7667	+1.0929%	+993000	+39910000	+0.2125	+7.8737%	+0.9791	+8.9666%	+8.9666%

Known prime factors (1 factor, 67.3 bits, 0.00400046% known):

Remaining cofactor is not a probable-prime

								GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
1681073	175584189046811897959	21	67.251	52223844249123 3 × 29 × 151 × 3301 × 1204279	3301	1204279	2012-02-18	28.079	0.0047	0.0084

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-24T11:29:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	1.046%
2012-02-18T13:08:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	1.536%
2012-02-18T13:08:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	2.140%
2012-02-18T13:08:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	2.547%
2012-02-18T13:09:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	2.859%
2012-02-18T13:09:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	3.115%
2012-02-18T13:09:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	3.332%
2012-02-18T13:09:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	3.522%
2012-02-18T13:09:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	3.690%
2012-02-18T13:09:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	3.842%
2012-02-18T13:09:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	3.981%
2012-02-18T13:10:00	Axon	Manual testing	1000000	16000000		-		-	-	0.124	-	-	7.846%
2012-02-18T13:10:00	Axon	Manual testing	1000000	24000000		-		-	-	0.154	-	-	8.414%
2012-02-18T13:10:00	Axon	Manual testing	1000000	32000000		-		-	-	0.183	-	-	8.817%
2012-02-18T13:10:00	Axon	Manual testing	1000000	40000000		-		-	-	0.213	-	-	9.129%
2016-03-17T19:18:39	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	7.326%

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	?	2⁵⁷		-	-	0.011	-	-
2003-03-27T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁸		-	-	0.023	-	-
2010-04-25T23:20:00	For Research	m1_76l	2⁶⁰	2⁶¹		-	-	0.091	-	-
2010-10-04T14:38:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.949	-	-

ECM factoring results:

ECM Summary

B1	B2	factor	curves	GHz-days
		175584189046811897959	1	0.00000e+0
50000	5000000		251	14.90

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	8F8E552F74850236	0.079

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T00:10:29

Oliver Kruse

GTX-1

175584189046811897959

061710A354108E__

no

2017-11-03T02:47:38

ATH

ec2-1xf

175584189046811897959

061710A354108E__

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 = 40000000 (stage 2)

B1 = 1000000, B2 = 32000000 (stage 2)

B1 = 1000000, B2 = 24000000 (stage 2)

B1 = 1000000, B2 = 16000000 (stage 2)

B1 = 500000, B2 = 15000000 (stage 2)

B1 = 1000000 (stage 1)

B1 = 900000 (stage 1)

B1 = 800000 (stage 1)

B1 = 700000 (stage 1)

B1 = 600000 (stage 1)

B1 = 500000 (stage 1)

B1 = 400000 (stage 1)

B1 = 300000 (stage 1)

B1 = 200000 (stage 1)

B1 = 100000 (stage 1)

B1 = 50000 (stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶³

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-01-20T12:09:55+00:00