M1647853 Mersenne number exponent details

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is 2 ^1647853 - 1

has 496054 decimal digits

takes 0.074 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	467E06F1AF42A3D9	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	2⁶⁸	36.1712	69.1176%	2000000	181263830	0.7621	7.9813%	36.9333	71.5825%	2.4648%
PrimeNet	2⁵⁷	0.0117	63.1579%	7000	120000	0.0009	2.5628%	0.0125	64.1021%	0.9442%
GPU72	2⁶¹	0.1864	65.5738%	6500	80000	0.0007	1.1718%	0.1871	65.9772%	0.4034%
Difference	+7	+35.9848	+3.5439%	+1993500	+181183830	+0.7614	+6.8096%	+36.7462	+5.6053%	+5.6053%

Known prime factors:
No known factors for M1647853

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T17:07:00	Axon	Manual testing	100000	100000		-		-	-	0.006	-	-	0.761%
2012-02-29T17:12:00	Axon	Manual testing	200000	200000		-		-	-	0.013	-	-	1.124%
2012-02-29T18:07:00	Axon	Manual testing	300000	300000		-		-	-	0.019	-	-	1.379%
2012-02-29T18:11:00	Axon	Manual testing	400000	400000		-		-	-	0.026	-	-	1.579%
2012-02-29T19:09:00	Axon	Manual testing	500000	500000		-		-	-	0.032	-	-	1.746%
2012-02-29T19:12:00	Axon	Manual testing	600000	600000		-		-	-	0.039	-	-	1.889%
2012-02-29T20:08:00	Axon	Manual testing	700000	700000		-		-	-	0.045	-	-	2.015%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.052	-	-	2.128%
2012-02-29T21:09:00	Axon	Manual testing	900000	900000		-		-	-	0.058	-	-	2.231%
2012-02-29T21:13:00	Axon	Manual testing	1000000	1000000		-		-	-	0.065	-	-	2.325%
2012-03-01T06:07:00	Axon	Manual testing	1000000	8000000		-		-	-	0.089	-	-	4.291%
2012-03-01T07:08:00	Axon	Manual testing	1000000	20000000		-		-	-	0.132	-	-	5.186%
2017-09-01T01:41:28	Jocelyn Larouche	low 4M	2000000	20000000	12	-		-	-	0.193	-	-	5.502%
2018-02-08T12:52:25	Jocelyn Larouche	low 4M	2000000	40000000	12	-		-	-	0.264	-	-	6.272%
2018-02-19T11:48:46	Jocelyn Larouche	low 4M	2000000	80000000	12	-		-	-	0.405	-	-	7.052%
2018-09-24T11:55:51	Jocelyn Larouche	low 4M	2000000	164785300	12	-		-	-	0.704	-	-	7.873%
2018-10-16T11:47:45	Jocelyn Larouche	low 4M	2000000	181263830	12	-		-	-	0.762	-	-	7.981%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-04-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.070	-	-
2010-04-30T08:40:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.093	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.186	-	-
2010-08-03T22:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.969	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.596	-	-
2015-05-06T17:29:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.191	-	-
2015-05-07T09:32:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.267	-	-
2015-10-11T16:52:32	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.535	-	-
2017-10-27T12:33:03	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	9.070	-	-
2019-07-31T09:42:10	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	18.14	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.745 GHz-days
Estimated T-Level:	25.000

Digits	B1	Curves	Complete	FacMiss
20	11000	280 / 100	2.800	5.996%
25	50000	280 / 280	1.000	36.722%

New Calculation Method

Total ECM effort:	15.745 GHz-days
Estimated T-Level:	25.000

Digits	B1	Complete	FacMiss
20	11000	10.769	0.002%
25	50000	0.996	36.919%
30	250000	0.063	93.908%
35	1000000	0.003	99.707%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	15.75

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	467E06F1AF42A3D9	0.074
2015-06-28T05:06:00	MadPoo	Manual testing	467E06F1AF42A3D9	0.074

PRP results:
No PRP results for M1647853

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 = 2000000, B2 = 181263830 (P-1 stage 2)

B1 = 2000000, B2 = 164785300 (P-1 stage 2)

B1 = 2000000, B2 = 80000000 (P-1 stage 2)

B1 = 2000000, B2 = 40000000 (P-1 stage 2)

B1 = 2000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

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)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-07-31T09:42:10+00:00