M2138569 Mersenne number exponent details

Residue

Status

L-L

C3D0B6A194F35101

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	13.8943	67.1642%	500000	15000000	0.1230	5.1645%	14.0173	68.8600%	1.6958%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7310%	0.0196	63.1049%	1.0359%
GPU72	2⁶²	0.2873	64.5161%	10000	150000	0.0017	1.4873%	0.2890	65.0439%	0.5278%
Difference	+5	+13.6070	+2.6481%	+490000	+14850000	+0.1213	+3.6771%	+13.7283	+3.8161%	+3.8161%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.8943

67.1642%

500000

15000000

0.1230

5.1645%

14.0173

68.8600%

1.6958%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

170000

0.0017

2.7310%

0.0196

63.1049%

1.0359%

GPU72

2⁶²

0.2873

64.5161%

10000

150000

0.0017

1.4873%

0.2890

65.0439%

0.5278%

Difference

+13.6070

+2.6481%

+490000

+14850000

+0.1213

+3.6771%

+13.7283

+3.8161%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2138569	276869338044410576072159	24	77.874	64732383674412791 34273 × 1888728260567	2013-04-21	34273	1888728260567	15,834	9,810.5	18,323

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2138569

276869338044410576072159

77.874

64732383674412791
34273 × 1888728260567

2013-04-21

34273

1888728260567

15,834

9,810.5

18,323

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.278%
2010-10-26T06:14:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.776%
2010-11-27T09:40:00	Oscar Östlin		80000	1500000		-		-	-	0.015	-	-	2.378%
2016-03-27T12:22:48	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.164%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T10:02:01	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.072	-	-
2009-01-04T22:08:00	Sturle Sunde	figaro.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-16T06:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.459	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.962 GHz-days
Estimated T-Level:	1.150

Digits	B1	Curves	Complete	FacMiss
20	11000	23 / 100	0.230	79.361%
25	50000	23 / 280	0.082	92.100%

New Calculation Method

Total ECM effort:	1.962 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.885	41.287%
25	50000	0.082	92.141%
30	250000	0.005	99.485%

ECM Summary

B1	B2	factor	curves	GHz-days
		276869338044410576072159	1	0.00000e+0
50000	5000000		23	1.962

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-31T16:27:00	dragon325	x-liberty	50000	5000000						3	0.256
2010-02-21T10:24:00	James Hintz	ryan	50000	5000000						3	0.256
2011-07-30T17:19:00	Andrew B	dell_xps_8100_i7_x86	50000	5000000						3	0.256
2013-04-21T07:07:00	Xyzzy	J			276869338044410576072159	77.874		1		1	-
2022-04-03T05:28:47	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.597
2022-07-13T02:34:04	MarkS	laptop64	50000	5000000						7	0.597

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	C3D0B6A194F35101	0.141

date

userid

compid

res64

spent (GHz-days)

1999-02-14T00:00:00

ANONYMOUS

v4_computers

C3D0B6A194F35101

0.141

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T17:23:43

Oliver Kruse

GTX-0

276869338044410576072159

350424152275FB__

2017-11-18T11:23:35

kkmrkkblmbrbk

old

276869338044410576072159

350424152275FB__

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 = 80000, B2 = 1500000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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