M2 208 977 Mersenne number exponent details

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M2208977

<<<

>>>

is 2 ^2208977 - 1

has 664969 decimal digits

takes 0.145 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	13.4514	67.1642%	500000	15000000	0.1230	5.1846%	13.5744	68.8666%
Target	2⁶²	0.2781	64.5161%	11000	850000	0.0054	1.6013%	0.2835	65.0843%
Difference	+5	+13.1733	+2.6481%	+489000	+14150000	+0.1176	+3.5833%	+13.2909	+3.7822%

Known prime factors (1 factor, 25.7 bits, 0.00116162% 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
2208977	53015449	8	25.660	12 2² × 3	-	4	4	2.029e-12	3.813e-7	7.761e-7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-04-17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 53015449	-	-	0.123	-	-	5.185%

Trial Factoring results:
No TF results for M2208977

ECM factoring results:

Total ECM effort:	14.675 GHz-days
Estimated T-Level:	21.763

Digits	B1	Complete	FacMiss
20	11000	3.716	2.434%
25	50000	0.353	70.293%
30	250000	0.023	97.768%
35	1000000	0.001	99.892%

ECM Summary

B1	B2	curves	GHz-days
50000	50000	16	0.812
50000	5000000	20	1.713
50000	20855730	50	9.88
50000	38914785	7	2.274

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-17	alpertron		50000	5000000						3	0.257
2018-09-28	alpertron	Manual testing	50000	5000000						3	0.257
2022-06-09	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.600
2022-08-05	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.600
2022-10-08	Naegi Makoto	1700	50000	38914785						7	2.274
2023-02-17	JackBlock	school2b	50000	50000						9	0.457
2023-04-06	JackBlock	school2b	50000	50000						7	0.355
2023-05-10	JacobZ	CServer	50000	20855730						50	9.88

Lucas-Lehmer results:
No L-L results for M2208977

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09

Oliver Kruse

53015449

049B91F9A04C22__

2017-11-20

kkmrkkblmbrbk

c4.xlarge

53015449

049B91F9A04C22__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

this exponent TF target: 62

TF double-checked to: 67.9

ECM T-Level=21.76 ~= 56-bit

2⁵⁰

2⁶⁰

2⁷⁰

JSON version of this page

Last modified: 2023-10-02T12:12:48+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