M2 047 729 Mersenne number exponent details

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M2047729

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>>>

is 2 ^2047729 - 1

has 616428 decimal digits

takes 0.135 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	14.5107	68.6567%	500000	15000000	0.1230	5.1376%	14.6337	70.2670%
Target	2⁶²	0.3000	66.1290%	9000	600000	0.0039	1.3300%	0.3039	66.5795%
Difference	+5	+14.2106	+2.5277%	+491000	+14400000	+0.1191	+3.8076%	+14.3297	+3.6875%

Known prime factors (2 factors, 80.4 bits, 0.00392795% 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
2047729	398369295119	12	38.535	97271 211 × 461	-	211	461	1.885e-8	2.141e-5	4.094e-5
2047729	4099336398727	13	41.899	1000947 3 × 109 × 3061	2008-07-15	109	3061	2.368e-7	2.573e-5	2.969e-5

exponent	prime factors	composite factor	digits	bits*
2047729	398369295119 4099336398727	1633049751616534918913513	25	80.434

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
2016-03-17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 398369295119 skipped known factor: 4099336398727	-	-	0.123	-	-	5.138%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15	J Feitsma	Manual testing	?	?	4099336398727	41.899	13	9.37328e-8	0.571	3.97333e-7

ECM factoring results:

Total ECM effort:	12.945 GHz-days
Estimated T-Level:	22.212

Digits	B1	Complete	FacMiss
20	11000	4.559	1.048%
25	50000	0.442	64.245%
30	250000	0.030	97.081%
35	1000000	0.001	99.852%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	20	1.697
50000	6750000	14	1.356
50000	6878530	7	0.684
50000	7000000	7	0.690
50000	27023535	7	1.656
67759	10009194	50	6.861

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-29	ATH	ec2-1xe	50000	5000000						3	0.254
2019-07-05	ATH	ec2-ECMCF	50000	5000000						3	0.254
2021-07-17	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.594
2021-10-02	happy5214	Focus	50000	6750000						7	0.678
2022-02-26	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.594
2022-06-01	Dylan Delgado	colab	50000	6750000						7	0.678
2022-08-01	MarkS	desktop-i7	50000	6878530						7	0.684
2022-10-10	BloodIce	Mjolnir4	50000	7000000						7	0.690
2022-12-20	Nesowa	309b3ECMtrial	50000	27023535						7	1.656
2023-11-06	debrouxl	dl380g9-1	67759	10009194						50	6.861

Lucas-Lehmer results:
No L-L results for M2047729

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06

Oliver Kruse

GTX-0

398369295119

4099336398727

88A2FD03DA94AF__

2017-11-15

kkmrkkblmbrbk

c4.xlarge

398369295119

4099336398727

88A2FD03DA94AF__

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)

10¹

10²

10³

10⁴

10⁵

10⁶

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=22.21 ~= 57-bit

2⁵⁰

2⁶⁰

2⁷⁰

JSON version of this page

Last modified: 2023-11-06T20:15:09+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
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0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront