M1904249 Mersenne number exponent details

Residue

Status

L-L

3C5FDE699BDF20BA

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	15.6040	68.6567%	500000	15000000	0.1015	5.0929%	15.7055	70.2530%	1.5963%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0393%	0.0114	64.2776%	1.1197%
GPU72	2⁶¹	0.1613	65.5738%	10000	160000	0.0014	1.7281%	0.1627	66.1687%	0.5949%
Difference	+6	+15.4427	+3.0829%	+490000	+14840000	+0.1000	+3.3648%	+15.5427	+4.0843%	+4.0843%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.6040

68.6567%

500000

15000000

0.1015

5.0929%

15.7055

70.2530%

1.5963%

PrimeNet

2⁵⁷

0.0101

63.1579%

9000

160000

0.0014

3.0393%

0.0114

64.2776%

1.1197%

GPU72

2⁶¹

0.1613

65.5738%

10000

160000

0.0014

1.7281%

0.1627

66.1687%

0.5949%

Difference

+15.4427

+3.0829%

+490000

+14840000

+0.1000

+3.3648%

+15.5427

+4.0843%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1904249	5210834081208341022841	22	72.142	1368212371703580 2² × 3 × 5 × 13 × 31 × 101 × 223 × 2512297	2010-11-27	223	2512297	554.40	0.0108	0.0201

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1904249

5210834081208341022841

72.142

1368212371703580
2² × 3 × 5 × 13 × 31 × 101 × 223 × 2512297

2010-11-27

223

2512297

554.40

0.0108

0.0201

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:40:59	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 5210834081208341022841	-	-	0.101	-	-	5.093%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:40:59

alpertron

Manual testing

500000

15000000

skipped known factor: 5210834081208341022841

0.101

-

-

5.093%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-01-02T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2022-03-08T23:25:32	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.060	-	-
2022-03-09T05:13:24	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.081	-	-
2009-05-23T17:55:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.081	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.723 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	19.723 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.714	0.016%
25	50000	0.790	45.367%
30	250000	0.049	95.226%
35	1000000	0.002	99.775%

ECM Summary

B1	B2	factor	curves	GHz-days
		5210834081208341022841	1	0.00000e+0
50000	5000000		20	1.388
50000	6600000		213	16.67
50000	6750000		21	1.661

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-03T21:05:00	Hoang Anh Vo	whiterose	50000	5000000						3	0.208
2009-07-27T19:25:00	James Hintz	11_071509	50000	5000000						3	0.208
2010-11-27T04:37:00	Chang Chia-Tche	sekhmet			5210834081208341022841	72.142		1		1	-
2020-11-01T08:19:59	Albrecht Heeffer	Ryzen5-factoring	50000	5000000						7	0.486
2021-01-22T11:04:27	Lisander Viaene	Asus_TUF_Gaming	50000	5000000						7	0.486
2021-05-03T19:33:47	nordi	sweet16	50000	6750000						7	0.554
2021-08-16T22:59:42	nordi	sweet16	50000	6750000						7	0.554
2021-11-25T08:12:06	Dylan Delgado	colab	50000	6750000						7	0.554
2021-12-17T10:36:59	TJAOI	Manual testing	50000	6600000						213	16.67

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	curtisc	v4_computers	3C5FDE699BDF20BA	0.103

date

userid

compid

res64

spent (GHz-days)

1999-01-02T00:00:00

curtisc

v4_computers

3C5FDE699BDF20BA

0.103

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

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