M4283 Mersenne number exponent details

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M4283

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is 2 ⁴²⁸³ - 1

has 1290 decimal digits

takes 0.000 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- L-L tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	6,937.6413	80.5970%	1000000000	201000000000	0.8572	16.8133%	6,938.4985	83.8593%	16.3593%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4333%	0.0000	68.2908%	0.7908%
GPU72	2⁴⁴	0.0005	70.4545%	500	10000	0.0000	0.9702%	0.0005	70.7412%	0.2867%
Difference	+23	+6,937.6407	+10.1425%	+999999500	+200999990000	+0.8572	+15.8431%	+6,938.4979	+13.1181%	+13.1181%

Known prime factors (2 factors, 315.3 bits, 7.36133048% 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
4283	80203116140787492698009223167	29	96.018	9362960091149602229513101 17 × 103 × 2683 × 185599 × 10738181037503	-	185599	10738181037503	6.959e+12	42.157	78.737
4283	10145818944810620866352664112841390099253015390559 47709872564246847	67	219.268	11844290152709106778371076480085676043956356981741 1593494345581 3 × 340981813 × 1121606762134329677 × 103232382038786235364092649643329727	2021-04-15	1121606762134329677	103232382038786235364092649643329727	3.471e+13	4.053e+23	7.569e+23

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
4283	80203116140787492698009223167 10145818944810620866352664112841390099253015390559 47709872564246847	81372629517404823398395214354820698455076901865158 808918670771238096106693579304231972899104449	95	315.286

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-11T00:00:00	ANONYMOUS	v4_computers	1000000	100000000		-		-	-	0.000	-	-	3.773%
2001-06-17T00:00:00	ANONYMOUS	v4_computers	43000000	4290000000		-		-	-	0.020	-	-	9.725%
2001-07-17T00:00:00	ANONYMOUS	v4_computers	3000000000	4290000000		-		-	-	0.221	-	-	10.807%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	1073741824	4290000000		-		-	-	0.090	-	-	10.845%
2002-08-03T00:00:00	ANONYMOUS	v4_computers	2147483648	4290000000		-		-	-	0.163	-	-	10.840%
2002-09-22T00:00:00	ANONYMOUS	v4_computers	3221225472	4290000000		-		-	-	0.236	-	-	10.797%
2003-01-09T00:00:00	ANONYMOUS	v4_computers	4290000000	2147483647		-		-	-	0.309	-	-	10.749%
2021-07-05T12:41:54	ViliamF	3	1000000000	201000000000		-		-	-	0.857	-	-	16.813%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-22T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.140	-	-
1999-12-23T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.280	-	-
2000-02-16T00:00:00	ANONYMOUS	v4_computers	2⁵⁴	2⁵⁵		-	-	0.560	-	-
2000-08-31T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁶		-	-	2.241	-	-
2003-01-16T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁷		-	-	4.483	-	-

ECM factoring results:

Total ECM effort:	25.052 GHz-days
Estimated T-Level:	33.247

Digits	B1	Curves	Complete	FacMiss
20	11000	1130 / 100	11.300	0.001%
25	50000	1130 / 280	4.036	1.755%
30	250000	1130 / 640	1.766	17.084%
35	1000000	1026 / 1580	0.649	52.227%
40	3000000	1026 / 4700	0.218	80.387%
45	11000000	415 / 9700	0.043	95.812%
50	44000000	201 / 17100	0.012	98.831%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		611	1.901
11000000	11000000		104	0.804
11000000	1100000000		214	2.441
44000000	4400000000		200	9.125
260000000	3142865025316	10145818944810620866352664112841390099253015390559 47709872564246847	1	10.78

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-04T15:12:00	unconnected	E5430-next	44000000	4400000000						200	9.125
2009-10-12T11:05:00	Carsten Kossendey	durandal	3000000	300000000						1	0.003
2009-10-13T13:31:00	Carsten Kossendey	durandal	3000000	300000000						1	0.003
2010-06-19T19:57:00	James Hintz	NEW_OMFG	3000000	300000000						609	1.894
2011-01-02T04:33:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-29T07:59:00	James Hintz	OMFG	11000000	1100000000						11	0.125
2016-10-03T02:29:46	kkmrkkblmbrbk	kel1	11000000	11000000						104	0.804
2020-03-21T20:52:37	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2020-08-12T23:25:18	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2021-04-15T23:46:11	Ryan Propper	Manual testing	260000000	3142865025316	10145818944810620866352664112841390099253015390559 47709872564246847	219.268	1	2	6655636513802850625	1	10.78

Lucas-Lehmer results:
Exponent "4283" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:33:48

Oliver Kruse

Oliver-PC

80203116140787492698009223167

665095E1DA15F9__

2017-09-21T19:21:11

Oliver Kruse

Manual testing

80203116140787492698009223167

665095E1DA15F9__

2017-10-12T13:52:42

kkmrkkblmbrbk

Manual testing

80203116140787492698009223167

665095E1DA15F9__

2020-04-17T12:32:22

Oliver Kruse

IOS-1

80203116140787492698009223167

B84DC619AA50CC__

2021-04-16T13:33:06

mnd9

75203

80203116140787492698009223167

10145818944810620866352664112841390099253015390559
47709872564246847

B84DC619AA50CC69

2021-04-16T14:28:18

_p95holder_

TFL3_PRPt20pE_h

80203116140787492698009223167

10145818944810620866352664112841390099253015390559
47709872564246847

B84DC619AA50CC69

2021-04-19T06:52:52

Klaus Nordmann

no1

80203116140787492698009223167

10145818944810620866352664112841390099253015390559
47709872564246847

B84DC619AA50CC69

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 = 1000000000, B2 = 201000000000 (stage 2)

B1 = 4290000000 (stage 1)

B1 = 3221225472, B2 = 4290000000 (stage 2)

B1 = 3221225472 (stage 1)

B1 = 3000000000, B2 = 4290000000 (stage 2)

B1 = 3000000000 (stage 1)

B1 = 2147483648, B2 = 4290000000 (stage 2)

B1 = 2147483648 (stage 1)

B1 = 1073741824, B2 = 4290000000 (stage 2)

B1 = 1073741824 (stage 1)

B1 = 1000000000 (stage 1)

B1 = 43000000, B2 = 4290000000 (stage 2)

B1 = 43000000 (stage 1)

B1 = 1000000, B2 = 100000000 (stage 2)

B1 = 1000000 (stage 1)

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TF factor-bounds graph:

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Last modified: 2021-07-05T12:41:54+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