M3429301 Mersenne number exponent details

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M3429301

<<<

>>>

is 2 ^3429301 - 1

has 1032323 decimal digits

takes 0.360 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- 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	Prob over default TF
Actual	2⁶⁹	34.8137	68.1159%	3429301	350377170	3.4009	9.0873%	38.2147	71.0133%	2.8974%
PrimeNet	2⁶⁰	0.0448	63.3333%	15000	280000	0.0045	2.8983%	0.0493	64.3960%	1.0627%
GPU72	2⁶⁴	1.0379	65.6250%	19000	320000	0.0054	1.8221%	1.0433	66.2513%	0.6263%
Difference	+5	+33.7758	+2.4909%	+3410301	+350057170	+3.3956	+7.2652%	+37.1714	+4.7620%	+4.7620%

Known prime factors (3 factors, 183.3 bits, 0.00534624% 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
3429301	301778489	9	28.169	44 2² × 11	-	4	11	1.053e-11	6.672e-7	1.240e-6
3429301	14399492251902629849	20	63.643	2099479201724 2² × 17² × 967 × 1051 × 1787	2017-04-03	1051	1787	0.8352	0.0002	0.0003
3429301	3567848019319312112957673143	28	91.527	520200475157956696271 7 × 23 × 31² × 17299 × 89561 × 2170109	2018-10-31	89561	2170109	197,861,667	0.0309	0.0336

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3429301	301778489 14399492251902629849	4345457014146383010957518161	28	91.812
3429301	301778489 3567848019319312112957673143	1076699784251824817967763922050420927	37	119.696
3429301	14399492251902629849 3567848019319312112957673143	51375199910154579184117590888922170345457445407	47	155.170
3429301	301778489 14399492251902629849 3567848019319312112957673143	15503930200959384662613859376779099405452755888724 450023	56	183.339

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-09-15T20:23:57	Jocelyn Larouche	Manual testing	345000	6858602	6	-	skipped known factor: 301778489 skipped known factor: 14399492251902629849 skipped known factor: 3567848019319312112957673143	-	-	0.107	-	-	3.667%
2022-01-04T08:23:57	Jocelyn Larouche	Manual testing	3429301	111907950		-	skipped known factor: 301778489 skipped known factor: 14399492251902629849 skipped known factor: 3567848019319312112957673143	-	-	1.422	-	-	7.706%
2022-08-16T01:28:00	Jocelyn Larouche	Manual testing	3429301	350377170		-	skipped known factor: 301778489 skipped known factor: 14399492251902629849 skipped known factor: 3567848019319312112957673143	-	-	3.401	-	-	9.087%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-05-01T06:50:31	LordJulius	Manual testing	2¹	2⁶²	301778489	28.169	9	1.05272e-11	0.776	2.26922e-11
2022-05-01T06:50:31	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.286	-	-
2017-04-03T15:15:04	TJAOI	Manual testing	2⁶³	2⁶⁴*	14399492251902629849	63.643	20	0.370	0.732	0.751
2022-05-01T06:50:31	LordJulius	Manual testing	2⁶³	2⁶⁴	14399492251902629849	63.643	20	0.370	0.732	0.751
2022-05-01T06:50:31	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.090	-	-
2022-05-01T06:50:31	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.179	-	-
2022-05-01T06:50:31	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.358	-	-
2021-04-10T02:19:14	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.716	-	-
2021-11-18T11:48:49	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	17.43	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.294 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.294 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	3567848019319312112957673143	2	0.294

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-31T21:59:35	ATH	ec2-ECMCF	50000	5000000	3567848019319312112957673143	91.527	2	2		2	0.294

Lucas-Lehmer results:
No L-L results for M3429301

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-06T11:18:44

Oliver Kruse

GTX-2

301778489

14399492251902629849

2DCB44E4B692C3__

2017-12-16T07:57:18

kkmrkkblmbrbk

c4.xlarge

301778489

14399492251902629849

2DCB44E4B692C3__

2018-11-04T16:52:04

Oliver Kruse

GTX-0

301778489

14399492251902629849

3567848019319312112957673143

2DCB44E4B692C3__

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 = 3429301, B2 = 350377170 (P-1 stage 2)

B1 = 3429301, B2 = 111907950 (P-1 stage 2)

B1 = 3429301 (P-1 stage 1)

B1 = 345000, B2 = 6858602 (P-1 stage 2)

B1 = 345000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-08-16T01:28:00+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