M3500779 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	2⁶⁸	17.0262	67.6471%	3000000	273000000	2.6971	9.4110%	19.7233	70.6918%	3.0447%
PrimeNet	2⁶⁰	0.0439	63.3333%	15000	300000	0.0046	2.9606%	0.0485	64.4189%	1.0855%
GPU72	2⁶⁴	1.0167	65.6250%	20000	360000	0.0059	1.9155%	1.0226	66.2834%	0.6584%
Difference	+4	+16.0095	+2.0221%	+2980000	+272640000	+2.6912	+7.4955%	+18.7007	+4.4084%	+4.4084%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.0262

67.6471%

3000000

273000000

2.6971

9.4110%

19.7233

70.6918%

3.0447%

PrimeNet

2⁶⁰

0.0439

63.3333%

15000

300000

0.0046

2.9606%

0.0485

64.4189%

1.0855%

GPU72

2⁶⁴

1.0167

65.6250%

20000

360000

0.0059

1.9155%

1.0226

66.2834%

0.6584%

Difference

+16.0095

+2.0221%

+2980000

+272640000

+2.6912

+7.4955%

+18.7007

+4.4084%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3500779	287063879	9	28.097	41 41	-	1	41	1.031e-11	4.842e-7	6.282e-7
3500779	560208658697	12	39.027	80012 2² × 83 × 241	2008-09-07	83	241	2.759e-8	1.395e-5	2.572e-5
3500779	244535613872491559831	21	67.729	34925885620385 5 × 37 × 188788570921	2022-01-13	37	188788570921	10.604	1,566.4	2,925.6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3500779

287063879

28.097

41
41

1.031e-11

4.842e-7

6.282e-7

3500779

560208658697

39.027

80012
2² × 83 × 241

2008-09-07

241

2.759e-8

1.395e-5

2.572e-5

3500779

244535613872491559831

67.729

34925885620385
5 × 37 × 188788570921

2022-01-13

188788570921

10.604

1,566.4

2,925.6

exponent	prime factors	composite factor	digits	bits*
3500779	287063879 560208658697	160815670614947905663	21	67.124
3500779	287063879 244535613872491559831	70197341871883638559847444449	29	95.825
3500779	560208658697 244535613872491559831	136990968251156002718377834000207	33	106.756
3500779	287063879 560208658697 244535613872491559831	39325158734142688374472085615717508222953	41	134.853

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-03-24T18:20:55	ViliamF	3	3000000	273000000		-	skipped known factor: 287063879 skipped known factor: 560208658697	-	-	2.697	-	-	9.411%
2022-03-25T11:24:39	Jocelyn Larouche	Manual testing	1000000	123342450		-	skipped known factor: 287063879 skipped known factor: 560208658697	-	-	1.167	-	-	7.610%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07T19:49:00	Will Edgington	Manual testing	?	?	560208658697	39.027	12	6.66553e-9	0.791	1.43355e-8
2022-01-13T18:44:35	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸	skipped known factors(?)	-	-	8.538	-	-
2022-01-13T18:44:35	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸	244535613872491559831	67.729	21	2.116	0.747	4.299

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.442 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.442 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.442

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-04T05:04:03	rucio		50000	5000000						3	0.442

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-07T18:46:24

Oliver Kruse

GTX-0

287063879

560208658697

FE3802074D4B82__

2017-12-17T03:06:34

kkmrkkblmbrbk

c4.xlarge

287063879

560208658697

FE3802074D4B82__

2022-02-03T14:41:04

RichD0

Linux-5

287063879

560208658697

244535613872491559831

FE3802074D4B8258

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 = 3000000, B2 = 273000000 (P-1 stage 2)

B1 = 1000000, B2 = 123342450 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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