M996529 Mersenne number exponent details

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M996529

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is 2 ⁹⁹⁶⁵²⁹ - 1

has 299986 decimal digits

takes 0.030 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	BBC05EA7F450711E	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	29.8174	70.1493%	2000000	50000000	0.1983	6.7406%	30.0158	72.1614%	2.0121%
PrimeNet	2⁴⁰	0.0000	50.0000%	9000	400000	0.0013	24.0392%	0.0013	62.0196%	12.0196%
GPU72	2⁴⁴	0.0000	54.5455%	16000	700000	0.0023	18.6605%	0.0023	63.0275%	8.4820%
Difference	+23	+29.8174	+15.6038%	+1984000	+49300000	+0.1961	-11.9199%	+30.0135	+9.1339%	+9.1339%

Known prime factors (1 factor, 60.9 bits, 0.00611573% 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
996529	2219644916469364393	19	60.945	1113688069524 2² × 3² × 30935779709	2008-02-07	9	30935779709	0.2630	72.435	135.29

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.001	-	-	0.217%
2002-03-03T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.459%
2002-05-05T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.823%
2002-08-10T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.009	-	-	1.985%
2003-02-02T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.018	-	-	2.780%
2003-08-31T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.036	-	-	3.703%
unknown			2000000	50000000		-		-	-	0.198	-	-	6.741%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.005	-	-
2000-10-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.010	-	-
2001-12-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.019	-	-
2003-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.039	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.305 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.305 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.692	0.000%
25	50000	1.609	20.008%
30	250000	0.131	87.737%
35	1000000	0.009	99.133%

ECM Summary

B1	B2	factor	curves	GHz-days
		2219644916469364393	1	0.00000e+0
50000	5000000		278	9.66
250000	25000000		44	7.645

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-17T02:03:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-02-07T00:02:00	Chad Davis	Bayes			2219644916469364393	60.945		1		1	-
2015-10-02T00:32:41	Richard B. Woods	Puttputt	50000	5000000						1	0.035
2016-09-23T16:25:28	TJAOI	Manual testing	50000	5000000						95	3.301
2017-01-27T18:38:14	TJAOI	Manual testing	50000	5000000						90	3.127
2017-09-15T15:41:25	TJAOI	Manual testing	50000	5000000						91	3.162
2020-01-27T11:13:15	TJAOI	Manual testing	250000	25000000						44	7.645

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-12-01T00:00:00	ANONYMOUS	v4_computers	BBC05EA7F450711E	0.030

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T15:26:24

Oliver Kruse

GTX-0

2219644916469364393

90E90C0CF746EF__

2017-10-15T13:03:06

Oliver Kruse

GTX-3

2219644916469364393

90E90C0CF746EF__

2017-12-24T11:22:40

ATH

ec2-1xf

2219644916469364393

90E90C0CF746EF__

2020-04-25T14:20:53

Oliver Kruse

AddPrpType5

2219644916469364393

827BE3F8423EE9__

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 = 50000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-25T14:20:53+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