M1851253 Mersenne number exponent details

Residue

Status

L-L

C24C379083E70F56

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	16.0507	68.6567%	500000	15000000	0.1015	5.0756%	16.1522	70.2476%	1.5909%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0235%	0.0117	64.2718%	1.1139%
GPU72	2⁶¹	0.1659	65.5738%	9000	150000	0.0013	1.6312%	0.1672	66.1353%	0.5616%
Difference	+6	+15.8848	+3.0829%	+491000	+14850000	+0.1002	+3.4444%	+15.9849	+4.1123%	+4.1123%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0507

68.6567%

500000

15000000

0.1015

5.0756%

16.1522

70.2476%

1.5909%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0235%

0.0117

64.2718%

1.1139%

GPU72

2⁶¹

0.1659

65.5738%

9000

150000

0.0013

1.6312%

0.1672

66.1353%

0.5616%

Difference

+15.8848

+3.0829%

+491000

+14850000

+0.1002

+3.4444%

+15.9849

+4.1123%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1851253	131355832513551377833	21	66.832	35477547507972 2² × 3³ × 23 × 1229 × 11621177	2013-09-15	1229	11621177	9.781	0.0499	0.0930

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1851253

131355832513551377833

66.832

35477547507972
2² × 3³ × 23 × 1229 × 11621177

2013-09-15

1229

11621177

9.781

0.0499

0.0930

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-03T15:46:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.923%
2016-03-16T12:35:48	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 131355832513551377833	-	-	0.101	-	-	5.076%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2010-04-12T14:11:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.083	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.862	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.630 GHz-days
Estimated T-Level:	24.804

Digits	B1	Curves	Complete	FacMiss
20	11000	269 / 100	2.690	6.697%
25	50000	269 / 280	0.961	38.196%

New Calculation Method

Total ECM effort:	20.630 GHz-days
Estimated T-Level:	24.804

Digits	B1	Complete	FacMiss
20	11000	9.187	0.010%
25	50000	0.833	43.495%
30	250000	0.052	94.980%
35	1000000	0.002	99.763%

ECM Summary

B1	B2	factor	curves	GHz-days
		131355832513551377833	1	0.00000e+0
50000	5000000		40	2.766
50000	6600000		222	17.31
50000	6750000		7	0.552

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-19T16:30:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-20T18:08:00	SubPrime	abd1	50000	5000000						3	0.207
2011-01-27T00:56:00	Lupo	yorick	50000	5000000						3	0.207
2012-07-10T02:13:00	fre_games	desktop	50000	5000000						3	0.207
2013-09-15T09:04:00	Chang Chia-Tche	exbpc13			131355832513551377833	66.832		1		1	-
2020-10-18T12:55:22	nordi	sweet16	50000	5000000						7	0.484
2021-01-08T20:03:48	Chang Chia-Tche	exbpc13	50000	5000000						7	0.484
2021-04-03T12:56:21	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.484
2021-07-16T06:33:17	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-09-30T06:26:20	Dylan Delgado	colab	50000	6750000						7	0.552
2021-10-07T10:31:06	TJAOI	Manual testing	50000	6600000						222	17.31

date	userid	compid	res64	spent (GHz-days)
1998-04-11T00:00:00	ANONYMOUS	v4_computers	C24C379083E70F56	0.100
1998-12-27T00:00:00	Ethan O'Connor	v4_computers	C24C379083E70F56	0.100

date

userid

compid

res64

spent (GHz-days)

1998-04-11T00:00:00

ANONYMOUS

v4_computers

C24C379083E70F56

0.100

1998-12-27T00:00:00

Ethan O'Connor

v4_computers

C24C379083E70F56

0.100

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 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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