M2 848 823 Mersenne number exponent details

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is 2 ^2848823 - 1

has 857582 decimal digits

takes 0.220 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	10.4302	67.1642%	360000	296091180	1.8448	8.0372%	12.2750	69.8033%
Target	2⁶³	0.5602	65.0794%	16000	260000	0.0033	1.8288%	0.5635	65.7180%
Difference	+4	+9.8700	+2.0848%	+344000	+295831180	+1.8415	+6.2084%	+11.7115	+4.0853%

Known prime factors (2 factors, 120.7 bits, 0.00423777% 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
2848823	66761688402737	14	45.924	11717416 2³ × 193 × 7589	-	193	7589	2.036e-6	6.674e-5	8.644e-5
2848823	32945424435918821503441	23	74.802	5782287006935640 2³ × 3² × 5 × 73259 × 219248261	2023-02-01	73259	219248261	2,005.8	1.3455	2.4986

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
2023-01-29	Lisander Viaene	Desktop	72000	281496600		-	skipped known factor: 66761688402737	-	-	1.725	-	-	5.996%
2023-02-01	USAFSS	6917th_Scty_Sq	360000	296091180			32945424435918821503441	23	74.802	1.845	0.440	3.690	8.037%

Trial Factoring results:
No TF results for M2848823

ECM factoring results:

Total ECM effort:	0.313 GHz-days
Estimated T-Level:	0.577

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.313

Lucas-Lehmer results:
No L-L results for M2848823

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-22

Oliver Kruse

GTX-1

66761688402737

1D8D95BAF895EB__

no

2017-12-07

kkmrkkblmbrbk

c4.xlarge

66761688402737

1D8D95BAF895EB__

no

2023-02-02

LordJulius

WhiteBox

66761688402737

32945424435918821503441

1D8D95BAF895EB9E

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 = 296091180 (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=0.58 ~= -15-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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