M1 051 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

Cofactor is a certified prime

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	-	-	-	-	0.0000	0.0000%
Target	2⁴⁴	0.0022	75.0000%	500	50000	0.0000	0.6157%	0.0022	75.1539%
Difference	-44	-0.0022	-75.0000%	-500	-50000	0.0000	-0.6157%	-0.0022	-75.1539%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

0.0000

0.0000%

Target

2⁴⁴

0.0022

75.0000%

500

50000

0.0000

0.6157%

0.0022

75.1539%

Difference

-44

-0.0022

-75.0000%

-500

-50000

0.0000

-0.6157%

-0.0022

-75.1539%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1051	3575503	7	21.770	1701 3⁵ × 7	-	243	243	3.637e-10	4.649e-9	9.462e-9
1051	21573801281844182793233754303617414455827438530123 4576636299249	63	207.069	10263463978041951852156876452719987847681940309288 0388504424 2³ × 7 × 3761 × 487306946197912402294074355828616432164789964166446939	2010-08-08	3761	487306946197912402294074355828616432164789964166446939	1.307e+14	5.079e+41	9.487e+41
1051	30501790606325684292149480855801973385632629941253 4951989303214657199	69	227.500	14510842343637337912535433328164592476514096071005 4686959706572149 3 × 13 × 89 × 22291 × 17590259 × 1459596053 × 953995682251 × 76569733338655747012082020517	2013-08-09	953995682251	76569733338655747012082020517	1.667e+14	7.981e+16	1.491e+17
1051	hide decimal representation P180 click to show decimal representation	180	594.661		2013-08-09

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1051

3575503

21.770

1701
3⁵ × 7

243

3.637e-10

4.649e-9

9.462e-9

1051

21573801281844182793233754303617414455827438530123
4576636299249

207.069

10263463978041951852156876452719987847681940309288
0388504424
2³ × 7 × 3761 × 487306946197912402294074355828616432164789964166446939

2010-08-08

3761

487306946197912402294074355828616432164789964166446939

1.307e+14

5.079e+41

9.487e+41

1051

30501790606325684292149480855801973385632629941253
4951989303214657199

227.500

14510842343637337912535433328164592476514096071005
4686959706572149
3 × 13 × 89 × 22291 × 17590259 × 1459596053 × 953995682251 × 76569733338655747012082020517

2013-08-09

953995682251

76569733338655747012082020517

1.667e+14

7.981e+16

1.491e+17

1051

P180

click to show decimal representation

180

594.661

2013-08-09

exponent	prime factors	composite factor	digits	bits*
1051	3575503 21573801281844182793233754303617414455827438530123 4576636299249	77137191204637721109755668213846976239054373946772 0132466817873697247	69	228.839
1051	3575503 30501790606325684292149480855801973385632629941253 4951989303214657199	10905924381828930316363334524836252324624962525284 16958442609611916458996097	76	249.270
1051	21573801281844182793233754303617414455827438530123 4576636299249 30501790606325684292149480855801973385632629941253 4951989303214657199	65803956928129190127785515278603442060331657794403 96080967805515534075393840380619093048278270651956 6749999087358017632285516143551	131	434.569
1051	3575503 21573801281844182793233754303617414455827438530123 4576636299249 30501790606325684292149480855801973385632629941253 4951989303214657199	23528224540839670368946749323519244289704202343886 47450868863152420863317290246242470905139810155088 30473321986845854118289759827815031153	138	456.339

ECM factoring results:

Total ECM effort:	21.545 GHz-days
Estimated T-Level:	42.064

Digits	B1	Complete	FacMiss
20	11000	150.500	0.000%
25	50000	60.200	0.000%
30	250000	21.500	0.000%
35	1000000	6.689	0.124%
40	3000000	1.760	17.200%
45	11000000	0.413	66.173%
50	44000000	0.087	91.654%
55	110000000	0.017	98.342%
60	260000000	0.003	99.706%

ECM Summary

B1	B2	factor	curves	GHz-days
		21573801281844182793233754303617414455827438530123 4576636299249	1	0.00000e+0
		30501790606325684292149480855801973385632629941253 4951989303214657199	1	0.00000e+0
260000000	26000000000		301	21.55

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-12	Carsten Kossendey	durandal	260000000	26000000000						1	0.072
2009-10-19	James Hintz	4115	260000000	26000000000						300	21.47
2010-08-08	ANONYMOUS	Manual testing			21573801281844182793233754303617414455827438530123 4576636299249	207.069		1		1	-
2013-08-09	Ryan Propper	Manual testing			30501790606325684292149480855801973385632629941253 4951989303214657199	227.500		1		1	-

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

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

10²⁵

10²⁶

10²⁷

10²⁸

10²⁹

10³⁰

10³¹

10³²

10³³

10³⁴

10³⁵

10³⁶

10³⁷

10³⁸

10³⁹

10⁴⁰

10⁴¹

10⁴²

10⁴³

10⁴⁴

10⁴⁵

10⁴⁶

10⁴⁷

10⁴⁸

10⁴⁹

10⁵⁰

10⁵¹

10⁵²

10⁵³

10⁵⁴

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=42.06 ~= 123-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

2¹⁶⁰

2¹⁷⁰

2¹⁸⁰

2¹⁹⁰

2²⁰⁰

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