M1630253 Mersenne number exponent details

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M1630253

<<<

>>>

is 2 ^1630253 - 1

has 490756 decimal digits

takes 0.073 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	970BCB53E1107A40	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	18.2266	68.6567%	1000000	20000000	0.1318	5.6800%	18.3584	70.4370%	1.7803%
PrimeNet	2⁵⁷	0.0118	63.1579%	7000	120000	0.0009	2.5574%	0.0126	64.1001%	0.9422%
GPU72	2⁶¹	0.1884	65.5738%	6500	70000	0.0006	1.1184%	0.1891	65.9588%	0.3850%
Difference	+6	+18.0381	+3.0829%	+993500	+19930000	+0.1312	+4.5616%	+18.1693	+4.4782%	+4.4782%

Known prime factors (1 factor, 78.5 bits, 0.00481827% 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
1630253	442477735341668047549817	24	78.550	135708302742478636 2² × 27986051 × 1212285209	2016-07-31	27986051	1212285209	37,680	5.9916	7.9896

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T16:07:00	Axon	Manual testing	100000	100000		-		-	-	0.006	-	-	0.876%
2012-02-29T17:11:00	Axon	Manual testing	200000	200000		-		-	-	0.013	-	-	1.279%
2012-02-29T18:05:00	Axon	Manual testing	300000	300000		-		-	-	0.019	-	-	1.559%
2012-02-29T18:11:00	Axon	Manual testing	400000	400000		-		-	-	0.026	-	-	1.779%
2012-02-29T19:07:00	Axon	Manual testing	500000	500000		-		-	-	0.032	-	-	1.961%
2012-02-29T19:11:00	Axon	Manual testing	600000	600000		-		-	-	0.039	-	-	2.117%
2012-02-29T20:06:00	Axon	Manual testing	700000	700000		-		-	-	0.045	-	-	2.254%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.052	-	-	2.377%
2012-02-29T21:06:00	Axon	Manual testing	900000	900000		-		-	-	0.058	-	-	2.488%
2012-02-29T21:12:00	Axon	Manual testing	1000000	1000000		-		-	-	0.065	-	-	2.590%
2012-03-01T06:05:00	Axon	Manual testing	1000000	8000000		-		-	-	0.089	-	-	4.716%
2012-03-01T07:07:00	Axon	Manual testing	1000000	20000000		-		-	-	0.132	-	-	5.680%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2016-02-23T16:28:42	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.071	-	-
2010-04-28T22:50:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.094	-	-
2016-02-23T16:28:42	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.188	-	-
2010-09-13T18:09:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.979	-	-
2016-02-23T16:28:42	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.602	-	-
2015-05-02T16:12:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.204	-	-
2015-05-03T12:18:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.292	-	-
2015-10-11T16:52:47	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.584	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.099 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:	14.099 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		248	13.93
50000	5000000	442477735341668047549817	3	0.169

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-04-30T22:02:00	Steve Scott	Celeron	50000	5000000						3	0.169
2009-06-20T13:47:00	freeshow	USB-key	50000	5000000						3	0.169
2010-05-03T09:47:00	Lukasz Wrobel	cm-3	50000	5000000						3	0.169
2011-09-08T17:02:00	S36049	Wolle5	50000	5000000						3	0.169
2013-04-29T15:58:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.169
2013-11-13T18:54:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.169
2014-06-17T05:44:00	mikr	MSI	50000	5000000						12	0.674
2016-03-31T10:23:15	Bruce	DESK3	50000	5000000						3	0.169
2016-05-09T08:25:58	Dennis Schreiber	z800	50000	5000000						3	0.169
2016-08-01T03:44:49	Bruce	DESK3	50000	5000000	442477735341668047549817	78.550	3	2		3	0.169
2019-10-28T14:13:16	TJAOI	Manual testing	50000	5000000						212	11.91

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	970BCB53E1107A40	0.073
2015-06-27T00:54:00	MadPoo	Manual testing	970BCB53E1107A40	0.073

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T15:49:43

Oliver Kruse

GTX-2

442477735341668047549817

B3422848AF76ED__

2017-11-01T20:09:57

kkmrkkblmbrbk

c4.xlarge

442477735341668047549817

B3422848AF76ED__

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)

10⁴

10⁵

10⁶

10⁷

10⁸

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-10-28T14:13:16+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