M2 831 971 Mersenne number exponent details

≡

is 2 ^2831971 - 1

has 852509 decimal digits

takes 0.219 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	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	10.4923	67.1642%	360000	287380170	1.7916	8.0017%	12.2839	69.7916%
Target	2⁶³	0.5636	65.0794%	16000	260000	0.0033	1.8268%	0.5669	65.7173%
Difference	+4	+9.9287	+2.0848%	+344000	+287120170	+1.7883	+6.1749%	+11.7171	+4.0743%

Known prime factors (2 factors, 128.6 bits, 0.00454170% 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
2831971	4464151346757671	16	51.987	788170385 5 × 491 × 321047	-	491	321047	0.0002	0.0020	0.0037
2831971	117129445697288173434617	24	76.632	20679845538193748 2² × 1283 × 299501 × 13454339	2023-01-31	299501	13454339	5,834.5	0.1138	0.1533

1 Composite Factors:

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2023-01-28	Lisander Viaene	Desktop	72000	281496600		-	skipped known factor: 4464151346757671	-	-	1.725	-	-	5.992%
2023-01-31	USAFSS	USAFSACS	360000	287380170			117129445697288173434617	24	76.632	1.792	0.437	3.583	8.002%

Trial Factoring results:
No TF results for M2831971

ECM factoring results:

Total ECM effort:	6.263 GHz-days
Estimated T-Level:	4.499

Digits	B1	Complete	FacMiss
20	11000	0.900	40.666%
25	50000	0.130	87.772%
30	250000	0.016	98.446%
35	1000000	0.002	99.835%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		10	1.044
250000	25000000		2	1.044
1000000	100000000		2	4.175

Lucas-Lehmer results:
No L-L results for M2831971

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-22

Oliver Kruse

GTX-3

4464151346757671

35BBF7CE52D03B__

no

2017-12-07

kkmrkkblmbrbk

c4.xlarge

4464151346757671

35BBF7CE52D03B__

no

2023-02-01

LordJulius

WhiteBox

4464151346757671

117129445697288173434617

35BBF7CE52D03BDF

no

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 = 360000, B2 = 287380170 (P-1 stage 2)

B1 = 72000, B2 = 281496600 (P-1 stage 2)

B1 = 360000 (P-1 stage 1)

B1 = 72000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

this exponent TF target: 63

TF double-checked to: 67.7

ECM T-Level=4.5 ~= -2-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-03-25T13:08:14+00:00