M2860133 Mersenne number exponent details

≡

M2860133

<<<

>>>

is 2 ^2860133 - 1

has 860986 decimal digits

takes 0.221 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	-unknown-	-unknown-
PRP	556F26538BFA99B3	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.8399	67.6471%	2870000	28700000	0.4790	6.4191%	21.3189	69.7238%	2.0768%
PrimeNet	2⁵⁹	0.0269	62.7119%	13000	240000	0.0028	2.9947%	0.0297	63.8285%	1.1167%
GPU72	2⁶³	0.5580	65.0794%	16000	280000	0.0034	1.8683%	0.5614	65.7318%	0.6524%
Difference	+5	+20.2819	+2.5677%	+2854000	+28420000	+0.4756	+4.5507%	+20.7575	+3.9920%	+3.9920%

Known prime factors (1 factor, 76.2 bits, 0.00266325% 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
2860133	85151999696520593038417	23	76.172	14886020981632776 2³ × 3 × 620250874234699	2020-10-03	8	620250874234699	10,048	3,784,555	7,068,496

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.244%
2009-07-03T00:45:00	Carsten Kossendey	leela	15000	157500		-		-	-	0.003	-	-	0.717%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.272%
2011-01-03T14:35:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.376%
2011-01-27T22:35:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.543%
2011-01-30T16:00:00	markr	tiny	105000	2257500		-		-	-	0.025	-	-	2.567%
2016-07-30T17:06:30	Jocelyn Larouche	Manual testing	174062	4515000	6	-		-	-	0.046	-	-	3.284%
2016-12-24T02:28:32	Jocelyn Larouche	low 4M	208874	208874		-		-	-	0.023	-	-	1.262%
2017-04-22T17:25:08	Jocelyn Larouche	low 4M	348124	3481240	6	-		-	-	0.058	-	-	3.417%
2019-10-23T02:43:14	masser	Manual testing	2870000	28700000	12	-		-	-	0.479	-	-	6.419%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:23	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-13T05:30:00	Sturle Sunde	aalto.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-01-25T07:47:00	lycorn	Manual testing	2⁶¹	2⁶²		-	-	0.107	-	-
2012-01-25T07:47:00	lycorn	Manual testing	2⁶²	2⁶³		-	-	0.343	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.686	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.306	-	-
2016-02-18T03:03:08	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	2.613	-	-
2017-11-12T17:07:16	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.225	-	-
2019-01-07T01:09:20	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.45	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.764 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	3.764 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.161	31.308%
25	50000	0.105	90.036%
30	250000	0.006	99.356%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		32	3.345
50000	5000000	85151999696520593038417	4	0.418

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-23T03:56:00	James Hintz	11_060902	50000	5000000						3	0.314
2010-12-06T10:28:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.314
2013-04-18T09:14:00	Donna Noble	PH2x6	50000	5000000						3	0.314
2015-07-01T00:58:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2016-09-12T15:20:48	Ismo Laitela		50000	5000000						3	0.314
2019-05-10T14:27:44	Claude Portenier	Petit-Idiot	50000	5000000						3	0.314
2020-08-23T18:37:20	mnd9	f4b	50000	5000000						7	0.732
2020-08-29T16:09:38	mnd9	libproj	50000	5000000						7	0.732
2020-10-03T01:22:10	mnd9	75203b	50000	5000000	85151999696520593038417	76.172	4	2	6022537132014255	4	0.418

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-30T00:00:00	ANONYMOUS	v4_computers	8B27CDB048FA07__	0.221

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-03T02:09:14

SRJ2877

85151999696520593038417

556F26538BFA99B3

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 = 2870000, B2 = 28700000 (P-1 stage 2)

B1 = 2870000 (P-1 stage 1)

B1 = 348124, B2 = 3481240 (P-1 stage 2)

B1 = 174062, B2 = 4515000 (P-1 stage 2)

B1 = 348124 (P-1 stage 1)

B1 = 105000, B2 = 2257500 (P-1 stage 2)

B1 = 208874 (P-1 stage 1)

B1 = 174062 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 157500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (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

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-10-03T02:09:14+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