M572791 Mersenne number exponent details

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M572791

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is 2 ⁵⁷²⁷⁹¹ - 1

has 172428 decimal digits

takes 0.008 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	51.8757	70.1493%	1500000	50000000	0.0876	6.1902%	51.9633	71.9971%	1.8478%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	200000	0.0003	20.0111%	0.0003	60.0055%	10.0055%
GPU72	2⁴⁴	0.0000	54.5455%	10000	340000	0.0006	15.2054%	0.0006	61.4570%	6.9115%
Difference	+23	+51.8757	+15.6038%	+1490000	+49660000	+0.0870	-9.0152%	+51.9627	+10.5401%	+10.5401%

Known prime factors (2 factors, 143.1 bits, 0.02497594% 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
572791	862442904756241894201	21	69.547	752842576748100 2² × 3 × 5² × 353 × 7108995059	2008-01-15	353	7108995059	221.98	8.1902	15.297
572791	13477073292228981804137	23	73.513	11764389884119148 2² × 111863 × 26291959549	2015-09-11	111863	26291959549	4,429.7	30.293	56.574

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
572791	862442904756241894201 13477073292228981804137	11623206237762731134924025906838127258109537	44	143.060

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.184%
2002-01-22T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.399%
2002-03-03T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.001	-	-	0.728%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.192%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.002	-	-	1.545%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.801%
2002-09-14T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.549%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.426%
unknown			1500000	50000000		-		-	-	0.088	-	-	6.190%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.004	-	-
2022-03-07T08:27:41	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.017	-	-
2002-01-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.034	-	-
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.067	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.327 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	424 / 100	4.240	1.410%
25	50000	424 / 280	1.514	21.937%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	17.327 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	24.769	0.000%
25	50000	3.131	4.366%
30	250000	0.300	74.067%
35	1000000	0.023	97.712%
40	3000000	0.001	99.851%

ECM Summary

B1	B2	factor	curves	GHz-days
		862442904756241894201	1	0.00000e+0
50000	5000000		223	3.613
50000	5000000	13477073292228981804137	57	0.924
250000	25000000		44	3.565
250000	35000000		100	9.225

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-20T22:18:00	Chad Davis	Bayes	50000	5000000						1	0.016
2007-10-01T22:17:00	ANONYMOUS	minister	50000	5000000						1	0.016
2008-01-15T06:16:00	Team_Bundu	bundu3			862442904756241894201	69.547		1		1	-
2015-06-07T14:22:00	Richard B. Woods	Puttputt	50000	5000000						2	0.032
2015-09-11T20:14:00	TJAOI	Manual testing	50000	5000000						40	0.648
2015-09-11T20:14:00	TJAOI	Manual testing	50000	5000000	13477073292228981804137	73.513	57	2		57	0.924
2016-04-01T10:53:20	TJAOI	Manual testing	50000	5000000						88	1.426
2017-05-12T15:31:02	TJAOI	Manual testing	50000	5000000						91	1.474
2018-08-03T12:20:48	TJAOI	Manual testing	250000	25000000						44	3.565
2021-06-11T13:26:48	TJAOI	Manual testing	250000	35000000						100	9.225

Lucas-Lehmer results:
No L-L results for M572791

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T11:24:37

Oliver Kruse

GTX-3

862442904756241894201

13477073292228981804137

B5BD090365EAA37D

2017-09-28T09:43:30

Oliver Kruse

Manual testing

862442904756241894201

13477073292228981804137

B5BD090365EAA3__

2017-09-30T15:28:21

alpertron

Manual testing

862442904756241894201

13477073292228981804137

B5BD090365EAA3__

2017-12-07T14:49:30

ATH

xps

862442904756241894201

13477073292228981804137

B5BD090365EAA3__

2020-04-19T08:52:27

Oliver Kruse

AddPrpType5

862442904756241894201

13477073292228981804137

7E8D323A728853__

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 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (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 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

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

B1 = 50000 (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 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T08:27:41+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