M1435339 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	20.7017	68.6567%	500000	15000000	0.0714	4.9221%	20.7731	70.1995%	1.5427%
PrimeNet	2⁵⁶	0.0067	62.5000%	6500	110000	0.0007	2.7756%	0.0074	63.5408%	1.0408%
GPU72	2⁶⁰	0.1070	65.0000%	6000	90000	0.0006	1.3541%	0.1076	65.4740%	0.4740%
Difference	+7	+20.5947	+3.6567%	+494000	+14910000	+0.0708	+3.5679%	+20.6655	+4.7255%	+4.7255%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.7017

68.6567%

500000

15000000

0.0714

4.9221%

20.7731

70.1995%

1.5427%

PrimeNet

2⁵⁶

0.0067

62.5000%

6500

110000

0.0007

2.7756%

0.0074

63.5408%

1.0408%

GPU72

2⁶⁰

0.1070

65.0000%

6000

90000

0.0006

1.3541%

0.1076

65.4740%

0.4740%

Difference

+20.5947

+3.6567%

+494000

+14910000

+0.0708

+3.5679%

+20.6655

+4.7255%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1435339	274634893583	12	37.999	95669 7 × 79 × 173	-	79	173	2.178e-8	4.657e-6	8.901e-6
1435339	17364597366854979377	20	63.913	6048953371592 2³ × 163 × 4638767923	2017-06-08	163	4638767923	1.9030	13.992	26.133
1435339	9998426566442259190057	22	73.082	3482949521486652 2² × 3 × 7 × 23 × 42589 × 42329449	2018-09-21	42589	42329449	2,617.0	0.1299	0.2385

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1435339

274634893583

37.999

95669
7 × 79 × 173

173

2.178e-8

4.657e-6

8.901e-6

1435339

17364597366854979377

63.913

6048953371592
2³ × 163 × 4638767923

2017-06-08

163

4638767923

1.9030

13.992

26.133

1435339

9998426566442259190057

73.082

3482949521486652
2² × 3 × 7 × 23 × 42589 × 42329449

2018-09-21

42589

42329449

2,617.0

0.1299

0.2385

exponent	prime factors	composite factor	digits	bits*
1435339	274634893583 17364597366854979377	4768924349957859272596054637791	31	101.912
1435339	274634893583 9998426566442259190057	2745916816072309931575407966704231	34	111.081
1435339	17364597366854979377 9998426566442259190057	173618651628336126439510127458649458454489	42	136.995
1435339	274634893583 17364597366854979377 9998426566442259190057	47681739913972041752069296541256960255549166163644 087	53	174.994

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:14:17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 274634893583	-	-	0.071	-	-	4.922%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-06-08T15:22:30	TJAOI	Manual testing	2⁶³	2⁶⁴*	17364597366854979377	63.913	20	0.791	0.111	1.608

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.483 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.483 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	11.81
50000	5000000	9998426566442259190057	1	0.047
250000	35000000		50	13.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-19T21:42:52	Oliver Kruse	ECM-HTC	50000	5000000						3	0.142
2018-09-21T13:05:40	Chang Chia-Tche	exbpc13	50000	5000000	9998426566442259190057	73.082	1	2		1	0.047
2018-11-24T16:18:48	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-02-15T12:28:35	TJAOI	Manual testing	50000	5000000						244	11.53
2021-11-26T09:13:23	TJAOI	Manual testing	250000	35000000						50	13.62

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:08

alpertron

Manual testing

274634893583

17364597366854979377

81EF743BCC711F__

2017-10-18T06:42:19

Oliver Kruse

Threadripper

274634893583

17364597366854979377

81EF743BCC711F__

2018-09-23T13:23:22

Oliver Kruse

GTX-5

274634893583

17364597366854979377

9998426566442259190057

C71000093D1C8B__

2018-09-23T13:32:14

ANONYMOUS

274634893583

17364597366854979377

9998426566442259190057

C71000093D1C8B__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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