M6029081 Mersenne number exponent details

Residue

Status

L-L

34154CB44E4C429E

double-checked

PRP

B88212C2C681C094

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷³	317.2696	68.4932%	2500000	50000000	1.3075	4.9531%	318.5771	70.0537%	1.5606%
PrimeNet	2⁶²	0.1019	62.9032%	26000	600000	0.0147	3.3323%	0.1166	64.1394%	1.2362%
GPU72	2⁶⁶	2.4495	65.1515%	40000	900000	0.0223	2.4191%	2.4719	65.9945%	0.8430%
Difference	+7	+314.8201	+3.3416%	+2460000	+49100000	+1.2851	+2.5340%	+316.1052	+4.0592%	+4.0592%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

317.2696

68.4932%

2500000

50000000

1.3075

4.9531%

318.5771

70.0537%

1.5606%

PrimeNet

2⁶²

0.1019

62.9032%

26000

600000

0.0147

3.3323%

0.1166

64.1394%

1.2362%

GPU72

2⁶⁶

2.4495

65.1515%

40000

900000

0.0223

2.4191%

2.4719

65.9945%

0.8430%

Difference

+314.8201

+3.3416%

+2460000

+49100000

+1.2851

+2.5340%

+316.1052

+4.0592%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6029081	43140908924620101672834086497	29	95.123	3577735058180517202608 2⁴ × 3² × 443 × 6427 × 124777 × 69935731	2021-12-10	124777	69935731	1.604e+9	1.0095	1.8288

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6029081

43140908924620101672834086497

95.123

3577735058180517202608
2⁴ × 3² × 443 × 6427 × 124777 × 69935731

2021-12-10

124777

69935731

1.604e+9

1.0095

1.8288

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2008-02-24T02:25:00	David Campeau	C0060	75000	1875000		-		-	-	0.044	-	-	1.377%
2013-02-21T19:51:00	Squeeky_Squirrel	P4_2600	110000	2172500		-		-	-	0.057	-	-	1.576%
2019-05-24T00:20:07	takahashi	vaio	400000	7500000	12	-		-	-	0.202	-	-	2.711%
2021-12-10T11:45:10	takahashi	vaio	2500000	50000000	12		43140908924620101672834086497	29	95.123	1.307	2.137	2.615	4.953%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.051	-	-
1998-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.102	-	-
2016-02-23T16:39:16	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.163	-	-
2014-09-12T10:05:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.326	-	-
2014-09-15T19:11:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.620	-	-
2015-10-05T01:56:43	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.239	-	-
2016-03-11T01:14:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.479	-	-
2018-05-29T09:13:08	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.958	-	-
2020-02-26T23:21:30	takahashi	Manual testing	2⁶⁸	2⁶⁹		-	-	9.92	-	-
2020-06-30T22:33:14	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	19.83	-	-
2021-01-18T11:40:52	takahashi	Manual testing	2⁷⁰	2⁷¹		-	-	39.66	-	-
2021-09-25T07:18:09	SRBase	Manual testing	2⁷¹	2⁷²		-	-	79.32	-	-
2021-12-01T21:17:47	takahashi	Manual testing	2⁷²	2⁷³		-	-	158.6	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.617 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.617 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.617

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-07-21T10:40:00	JimBa	Dell	50000	5000000						3	0.808
2016-06-17T01:36:35	vats09	AX2_64_10	50000	5000000						3	0.808

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-14T00:00:00	ANONYMOUS	v4_computers	34154CB44E4C429E	1.068
1998-12-27T00:00:00	ANONYMOUS	v4_computers	34154CB44E4C429E	1.068
1999-01-02T00:00:00	ANONYMOUS	v4_computers	34154CB44E4C429E	1.068
1999-03-01T00:00:00	ANONYMOUS	v4_computers	34154CB44E4C429E	1.068
1999-05-09T00:00:00	ANONYMOUS	v4_computers	34154CB44E4C429E	1.068
2000-12-21T00:00:00	Salz	v4_computers	34154CB44E4C429E	1.068

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 = 2500000, B2 = 50000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 400000, B2 = 7500000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 110000, B2 = 2172500 (P-1 stage 2)

B1 = 75000, B2 = 1875000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 75000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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