M1235093 Mersenne number exponent details

Residue

Status

L-L

2A8465E1252BDEF3

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	24.0580	68.6567%	300000	10000000	0.0368	4.1767%	24.0949	69.9658%	1.3091%
PrimeNet	2⁵⁶	0.0078	62.5000%	5500	90000	0.0004	2.4305%	0.0082	63.4114%	0.9114%
GPU72	2⁶⁰	0.1244	65.0000%	5000	30000	0.0003	0.8313%	0.1246	65.2910%	0.2910%
Difference	+7	+23.9337	+3.6567%	+295000	+9970000	+0.0366	+3.3454%	+23.9702	+4.6749%	+4.6749%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

24.0580

68.6567%

300000

10000000

0.0368

4.1767%

24.0949

69.9658%

1.3091%

PrimeNet

2⁵⁶

0.0078

62.5000%

5500

90000

0.0004

2.4305%

0.0082

63.4114%

0.9114%

GPU72

2⁶⁰

0.1244

65.0000%

5000

30000

0.0003

0.8313%

0.1246

65.2910%

0.2910%

Difference

+23.9337

+3.6567%

+295000

+9970000

+0.0366

+3.3454%

+23.9702

+4.6749%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1235093	316289807426061977	18	58.134	128042911516 2² × 13² × 189412591	2007-11-06	169	189412591	0.0595	0.4589	0.8571
1235093	259404332690061048445391	24	77.780	105014089096959115 5 × 19 × 1105411464178517	2017-10-13	19	1105411464178517	27,652	2,678,044	5,001,839

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1235093

316289807426061977

58.134

128042911516
2² × 13² × 189412591

2007-11-06

169

189412591

0.0595

0.4589

0.8571

1235093

259404332690061048445391

77.780

105014089096959115
5 × 19 × 1105411464178517

2017-10-13

1105411464178517

27,652

2,678,044

5,001,839

exponent	prime factors	composite factor	digits	bits*
1235093	316289807426061977 259404332690061048445391	82046946432025522659303507980873065998007	41	135.914

exponent

prime factors

composite factor

digits

bits*

1235093

316289807426061977
259404332690061048445391

82046946432025522659303507980873065998007

135.914

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-10-07T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.44667e-5	-	-	0.006%
2002-12-25T00:00:00	ANONYMOUS	v4_computers	20000	395000		-		-	-	0.002	-	-	1.041%
2016-03-17T19:02:38	alpertron	Manual testing	300000	10000000	12	-		-	-	0.037	-	-	4.177%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.016	-	-
2003-05-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.031	-	-
2022-04-13T05:54:05	LordJulius	Manual testing	2¹	2⁶¹	316289807426061977	58.134	18	0.059	0.077	0.121
2022-04-13T05:54:05	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.249	-	-
2022-04-13T05:54:05	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.795	-	-
2022-04-13T05:54:05	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	1.590	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.554 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	18.554 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		316289807426061977	1	0.00000e+0
50000	5000000		269	9.96
50000	5000000	259404332690061048445391	12	0.444
250000	25000000		44	8.148

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-06T15:23:00	Chad Davis	Bayes			316289807426061977	58.134		1		1	-
2017-10-13T13:39:11	TJAOI	Manual testing	50000	5000000	259404332690061048445391	77.780	12	2		12	0.444
2017-10-13T13:39:12	TJAOI	Manual testing	50000	5000000						128	4.740
2018-09-14T13:14:53	TJAOI	Manual testing	50000	5000000						141	5.222
2020-11-20T10:37:06	TJAOI	Manual testing	250000	25000000						44	8.148

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T16:55:59

Oliver Kruse

GTX-3

316289807426061977

67A75DD3A3771E__

2017-10-13T21:21:16

Oliver Kruse

GTX-1

99D4966EDD5F9D__

2017-10-14T21:59:36

YarBer

Manual testing

316289807426061977

259404332690061048445391

6B94C7AC868720__

2017-10-20T01:46:49

kkmrkkblmbrbk

c4.xlarge

316289807426061977

259404332690061048445391

99D4966EDD5F9D__

2017-11-04T14:28:47

kkmrkkblmbrbk

c4.xlarge

316289807426061977

259404332690061048445391

6B94C7AC868720__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 20000, B2 = 395000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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