M2048369 Mersenne number exponent details

Residue

Status

L-L

F12CC7CE677FB540

double-checked

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	2⁶⁷	14.5061	68.6567%	500000	15000000	0.1230	5.1378%	14.6291	70.2671%	1.6104%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6652%	0.0204	64.7581%	0.9650%
GPU72	2⁶²	0.2999	66.1290%	9000	120000	0.0014	1.3301%	0.3014	66.5795%	0.4505%
Difference	+5	+14.2062	+2.5277%	+491000	+14880000	+0.1216	+3.8077%	+14.3278	+3.6875%	+3.6875%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.5061

68.6567%

500000

15000000

0.1230

5.1378%

14.6291

70.2671%

1.6104%

PrimeNet

2⁵⁸

0.0187

63.7931%

9000

160000

0.0016

2.6652%

0.0204

64.7581%

0.9650%

GPU72

2⁶²

0.2999

66.1290%

9000

120000

0.0014

1.3301%

0.3014

66.5795%

0.4505%

Difference

+14.2062

+2.5277%

+491000

+14880000

+0.1216

+3.8077%

+14.3278

+3.6875%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2048369	1324909068083750687	19	60.201	323405858047 1097 × 294809351	2016-01-20	1097	294809351	0.1481	1.5314	2.8601
2048369	4359513082380972223	19	61.919	1064142515919 3 × 7 × 187181 × 270719	2008-12-07	187181	270719	0.2856	0.0183	0.0363

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2048369

1324909068083750687

60.201

323405858047
1097 × 294809351

2016-01-20

1097

294809351

0.1481

1.5314

2.8601

2048369

4359513082380972223

61.919

1064142515919
3 × 7 × 187181 × 270719

2008-12-07

187181

270719

0.2856

0.0183

0.0363

exponent	prime factors	composite factor	digits	bits*
2048369	1324909068083750687 4359513082380972223	5775958415276293344543712183404167201	37	122.119

exponent

prime factors

composite factor

digits

bits*

2048369

1324909068083750687
4359513082380972223

5775958415276293344543712183404167201

122.119

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	9.53375e-5	-	-	0.007%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.022%
2003-01-16T00:00:00	ANONYMOUS	v4_computers	25000	425000		-		-	-	0.004	-	-	1.261%
2016-03-17T19:20:05	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 4359513082380972223	-	-	0.123	-	-	5.138%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	Martijn Otto	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T08:13:22	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.075	-	-
2016-01-20T12:14:46	TJAOI	Manual testing	2⁶⁰	2⁶¹*	1324909068083750687	60.201	19	0.073	0.274	0.149

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.500 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	3.500 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.529	21.679%
25	50000	0.142	86.789%
30	250000	0.009	99.105%

ECM Summary

B1	B2	factor	curves	GHz-days
		4359513082380972223	1	0.00000e+0
50000	5000000		17	1.442
50000	6750000		7	0.678
50000	6885886		7	0.685
50000	7099496		7	0.695

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-07T12:26:00	SubPrime	dijkstra			4359513082380972223	61.919		1		1	-
2018-11-23T04:58:00	rucio		50000	5000000						3	0.254
2021-07-10T05:24:01	Deufo	Ryzen2600	50000	6750000						7	0.678
2021-09-29T03:14:40	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.594
2022-02-06T20:06:50	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.594
2022-05-26T21:34:53	debrouxl	dl380g9-1	50000	6885886						7	0.685
2022-07-26T17:30:02	debrouxl	dl380g9-1	50000	7099496						7	0.695

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	Martijn Otto	v4_computers	F12CC7CE677FB540	0.135

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

Martijn Otto

v4_computers

F12CC7CE677FB540

0.135

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:33:30

alpertron

Manual testing

1324909068083750687

4359513082380972223

B36A05F56CD93C__

2017-10-21T02:12:39

Oliver Kruse

Threadripper

1324909068083750687

4359513082380972223

B36A05F56CD93C__

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)

B1 = 25000, B2 = 425000 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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