M5034919 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

04775FE5DBFA594D

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	2⁷²	189.9402	68.0556%	300000	9375000	0.1597	2.9451%	190.0999	68.9964%	0.9408%
PrimeNet	2⁶¹	0.0610	62.2951%	22000	450000	0.0091	3.3171%	0.0701	63.5458%	1.2507%
GPU72	2⁶⁵	1.4490	64.6154%	34000	700000	0.0141	2.4188%	1.4631	65.4713%	0.8559%
Difference	+7	+188.4912	+3.4402%	+266000	+8675000	+0.1455	+0.5263%	+188.6367	+3.5251%	+3.5251%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

189.9402

68.0556%

300000

9375000

0.1597

2.9451%

190.0999

68.9964%

0.9408%

PrimeNet

2⁶¹

0.0610

62.2951%

22000

450000

0.0091

3.3171%

0.0701

63.5458%

1.2507%

GPU72

2⁶⁵

1.4490

64.6154%

34000

700000

0.0141

2.4188%

1.4631

65.4713%

0.8559%

Difference

+188.4912

+3.4402%

+266000

+8675000

+0.1455

+0.5263%

+188.6367

+3.5251%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5034919	762771192468712046879569	24	79.336	75748109599053336 2³ × 3 × 1601 × 32089 × 61434601	2021-10-26	32089	61434601	44,086	0.6788	1.2565

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5034919

762771192468712046879569

79.336

75748109599053336
2³ × 3 × 1601 × 32089 × 61434601

2021-10-26

32089

61434601

44,086

0.6788

1.2565

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.008%
2009-07-21T14:51:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	1.154%
2014-11-17T02:17:00	Jocelyn Larouche	Manual testing	67748	67748		-		-	-	0.014	-	-	0.406%
2017-02-19T18:35:04	Squeeky_Squirrel	i5-5250U_1600	300000	9375000	12	-		-	-	0.160	-	-	2.945%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-10-26T16:37:37	ATH	5960X	2500000	92500000	2	7	762771192468712046879569	P-1	24	79.336	1.730

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2016-02-23T16:39:07	Mark Rose	Manual testing	2⁶¹	2⁶³		-	-	0.256	-	-
2014-12-16T14:36:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.390	-	-
2014-12-16T14:36:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.742	-	-
2015-07-28T21:27:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.484	-	-
2016-05-17T12:45:08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.968	-	-
2018-06-11T12:29:24	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.937	-	-
2021-01-18T12:08:21	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.87	-	-
2021-04-01T15:52:30	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.75	-	-
2021-04-01T15:52:30	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.49	-	-
2021-04-03T17:57:01	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.99	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-09-02T15:16:00	S00030	vd01	50000	5000000						3	0.632
2014-05-25T10:58:00	exhopp	9007	50000	5000000						3	0.632
2017-06-26T22:12:19	deo2016	deo2016.home.new	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	DB83BD5DD198E2__	0.698
2000-04-27T00:00:00	akohler	v4_computers	9DCC6C4215DEFF__	0.698

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 = 92500000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 300000, B2 = 9375000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 67748 (P-1 stage 1)

B1 = 55000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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