M2900857 Mersenne number exponent details

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M2900857

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>>>

is 2 ^2900857 - 1

has 873245 decimal digits

takes 0.224 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	7D1FA3C3A86A2561	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	2⁶⁸	20.5473	67.6471%	2900857	5801714	0.3426	4.4808%	20.8899	69.0967%	1.4497%
PrimeNet	2⁵⁹	0.0265	62.7119%	13000	240000	0.0028	3.0023%	0.0293	63.8314%	1.1195%
GPU72	2⁶³	0.5502	65.0794%	16000	300000	0.0035	1.9091%	0.5537	65.7460%	0.6667%
Difference	+5	+19.9971	+2.5677%	+2884857	+5501714	+0.3390	+2.5717%	+20.3362	+3.3507%	+3.3507%

Known prime factors (1 factor, 68.1 bits, 0.00234923% 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
2900857	327014270192082722911	21	68.148	56365113859815 3 × 5 × 107 × 967 × 36316909	2019-07-03	967	36316909	24.629	0.2217	0.4139

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-04-27T00:00:00	ANONYMOUS	v4_computers	15000	150000		-		-	-	0.003	-	-	0.707%
2002-01-02T00:00:00	ANONYMOUS	v4_computers	20000	240000		-		-	-	0.004	-	-	0.912%
2002-01-02T00:00:00	ANONYMOUS	v4_computers	50000	1500000		-		-	-	0.014	-	-	1.978%
2010-03-21T13:20:00	Rob_Dee	twopc	100000	200000		-		-	-	0.012	-	-	1.200%
2010-03-22T14:47:00	Rob_Dee	twopc	200000	300000		-		-	-	0.023	-	-	1.499%
2010-03-23T15:26:00	Rob_Dee	twopc	300000	400000		-		-	-	0.034	-	-	1.720%
2010-03-24T14:32:00	Rob_Dee	twopc	400000	500000		-		-	-	0.045	-	-	1.900%
2010-03-25T15:10:00	Rob_Dee	twopc	500000	600000		-		-	-	0.057	-	-	2.053%
2010-03-26T13:53:00	Rob_Dee	twopc	600000	700000		-		-	-	0.068	-	-	2.188%
2010-03-27T14:04:00	Rob_Dee	twopc	700000	800000		-		-	-	0.079	-	-	2.308%
2010-03-28T14:44:00	Rob_Dee	twopc	800000	900000		-		-	-	0.090	-	-	2.417%
2010-03-29T13:40:00	Rob_Dee	twopc	900000	1000000		-		-	-	0.101	-	-	2.517%
2010-03-30T13:45:00	Rob_Dee	twopc	1000000	1100000		-		-	-	0.113	-	-	2.609%
2018-02-05T00:23:54	Jocelyn Larouche	low 4M	1440000	1440000		-		-	-	0.161	-	-	2.877%
2018-02-07T23:08:42	Jocelyn Larouche	low 4M	1728000	1728000		-		-	-	0.194	-	-	3.067%
2018-02-11T21:50:39	Jocelyn Larouche	low 4M	2073600	2073600		-		-	-	0.232	-	-	3.264%
2018-02-12T23:18:34	Jocelyn Larouche	low 4M	2488320	2488320		-		-	-	0.279	-	-	3.468%
2018-02-17T12:57:15	Jocelyn Larouche	low 4M	2900857	2900857		-		-	-	0.325	-	-	3.643%
2018-02-18T21:32:12	Jocelyn Larouche	low 4M	2900857	5801714	6	-		-	-	0.343	-	-	4.481%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
2016-02-23T16:29:24	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.026	-	-
2009-02-13T05:02:00	Sturle Sunde	gowin.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2011-12-07T21:05:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.106	-	-
2013-01-10T10:25:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.338	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.677	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.288	-	-
2016-02-20T17:30:30	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	2.576	-	-
2017-11-16T23:15:03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.152	-	-
2018-12-17T01:16:47	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.30	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.677 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	1.677 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.615	54.043%
25	50000	0.057	94.465%
30	250000	0.004	99.641%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.572
50000	5000000	327014270192082722911	1	0.105

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-26T19:36:00	S36049	Wolle3	50000	5000000						3	0.314
2011-03-16T06:02:00	Thomas N	ubuntu	50000	5000000						3	0.314
2013-05-25T22:31:00	Pool Party	St.P.p	50000	5000000						3	0.314
2015-12-21T02:48:00	Bruce	Desk7	50000	5000000						3	0.314
2016-09-17T05:25:45	Bruce	test	50000	5000000						3	0.314
2019-07-04T02:25:10	Corey	Computer	50000	5000000	327014270192082722911	68.148	1	2		1	0.105

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-23T00:00:00	ANONYMOUS	v4_computers	C58B6265CAED71__	0.224
1999-08-16T00:00:00	ANONYMOUS	v4_computers	7D1FA3C3A86A2561	0.224
2000-05-05T00:00:00	ANONYMOUS	v4_computers	7D1FA3C3A86A2561	0.224
2018-09-30T10:42:40	kkmrkkblmbrbk	old	7D1FA3C3A86A2561	0.224

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-07-09T06:13:10

roemer2201

ws-rebentrost-o

327014270192082722911

11A822BA68CBD7DC

2019-07-10T03:11:25

marssystems

system11

327014270192082722911

11A822BA68CBD7DC

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 = 2900857, B2 = 5801714 (P-1 stage 2)

B1 = 2900857 (P-1 stage 1)

B1 = 2488320 (P-1 stage 1)

B1 = 2073600 (P-1 stage 1)

B1 = 1728000 (P-1 stage 1)

B1 = 1440000 (P-1 stage 1)

B1 = 1000000, B2 = 1100000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000, B2 = 1000000 (P-1 stage 2)

B1 = 900000 (P-1 stage 1)

B1 = 800000, B2 = 900000 (P-1 stage 2)

B1 = 800000 (P-1 stage 1)

B1 = 700000, B2 = 800000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 600000, B2 = 700000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 500000, B2 = 600000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 400000, B2 = 500000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 300000, B2 = 400000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

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

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 15000, B2 = 150000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-07-10T03:11:25+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