M992863 Mersenne number exponent details

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M992863

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is 2 ⁹⁹²⁸⁶³ - 1

has 298882 decimal digits

takes 0.024 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality 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	29.9275	70.1493%	2000000	50000000	0.1623	6.7380%	30.0898	72.1606%	2.0113%
PrimeNet	2⁴⁰	0.0000	50.0000%	9000	400000	0.0011	24.0303%	0.0011	62.0152%	12.0152%
GPU72	2⁴⁴	0.0000	54.5455%	16000	650000	0.0018	18.4632%	0.0018	62.9378%	8.3924%
Difference	+23	+29.9275	+15.6038%	+1984000	+49350000	+0.1605	-11.7253%	+30.0880	+9.2228%	+9.2228%

Known prime factors (2 factors, 133.0 bits, 0.01339551% 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
992863	69756488494739049391	20	65.919	35128959632265 3 × 5 × 2341930642151	2007-09-16	5	2341930642151	7.9102	4,486.6	8,379.6
992863	156000566977940479799	21	67.080	78560973154373 3079 × 25515093587	2016-10-14	3079	25515093587	54.123	48.881	91.295

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
992863	69756488494739049391 156000566977940479799	10882051755569473554936484554735698752409	41	132.999

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		-		-	-	0.000	-	-	0.217%
2002-03-03T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.459%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.329%
2002-08-10T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.983%
2003-01-25T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.015	-	-	2.779%
2003-09-09T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.701%
unknown			2000000	50000000		-		-	-	0.162	-	-	6.738%

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:	14.237 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	14.237 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		69756488494739049391	1	0.00000e+0
50000	5000000		279	7.928
50000	5000000	156000566977940479799	2	0.057
250000	25000000		44	6.252

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-16T08:50:00	Chad Davis	Bayes			69756488494739049391	65.919		1		1	-
2015-12-21T09:07:38	Richard B. Woods	Puttputt	50000	5000000						1	0.028
2016-10-14T16:25:10	TJAOI	Manual testing	50000	5000000						97	2.756
2016-10-14T16:25:10	TJAOI	Manual testing	50000	5000000	156000566977940479799	67.080	2	2		2	0.057
2017-01-20T21:26:30	TJAOI	Manual testing	50000	5000000						90	2.558
2017-09-29T10:33:12	TJAOI	Manual testing	50000	5000000						91	2.586
2020-01-20T12:08:47	TJAOI	Manual testing	250000	25000000						44	6.252

Lucas-Lehmer results:
No L-L results for M992863

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T15:07:13

Oliver Kruse

GTX-0

69756488494739049391

156000566977940479799

B3A5B34109B83752

2017-10-05T21:00:49

Oliver Kruse

Manual testing

69756488494739049391

156000566977940479799

B3A5B34109B837__

2017-10-15T12:24:42

Oliver Kruse

GTX-3

69756488494739049391

156000566977940479799

B3A5B34109B837__

2017-12-24T02:01:41

ATH

ec2-1xf

69756488494739049391

156000566977940479799

B3A5B34109B837__

2020-04-25T01:30:39

Oliver Kruse

AddPrpType5

69756488494739049391

156000566977940479799

43B873CB6A1B8F__

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 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

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

B1 = 16384 (P-1 stage 1)

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

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-25T01:30:39+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