M500807 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	59.3321	71.6418%	1500000	50000000	0.0707	6.1004%	59.4028	73.3718%	1.7300%
PrimeNet	2⁴⁰	0.0000	52.5000%	5000	170000	0.0002	19.1045%	0.0002	61.5746%	9.0746%
GPU72	2⁴⁴	0.0000	56.8182%	9000	280000	0.0004	14.3594%	0.0004	63.0188%	6.2007%
Difference	+23	+59.3321	+14.8236%	+1491000	+49720000	+0.0703	-8.2591%	+59.4024	+10.3529%	+10.3529%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

59.3321

71.6418%

1500000

50000000

0.0707

6.1004%

59.4028

73.3718%

1.7300%

PrimeNet

2⁴⁰

0.0000

52.5000%

5000

170000

0.0002

19.1045%

0.0002

61.5746%

9.0746%

GPU72

2⁴⁴

0.0000

56.8182%

9000

280000

0.0004

14.3594%

0.0004

63.0188%

6.2007%

Difference

+23

+59.3321

+14.8236%

+1491000

+49720000

+0.0703

-8.2591%

+59.4024

+10.3529%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
500807	24038737	8	24.519	24 2³ × 3	-	8	8	4.486e-12	1.366e-7	2.780e-7
500807	16251472609991	14	43.886	16225285 5 × 3245057	2008-07-21	5	3245057	4.601e-6	0.0030	0.0056
500807	5769312617530563727343449	25	82.255	5760015951784383732 2² × 3 × 102031 × 4704465596881	2020-07-21	102031	4704465596881	2,697,448	4,377.2	8,175.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

500807

24038737

24.519

24
2³ × 3

4.486e-12

1.366e-7

2.780e-7

500807

16251472609991

43.886

16225285
5 × 3245057

2008-07-21

3245057

4.601e-6

0.0030

0.0056

500807

5769312617530563727343449

82.255

5760015951784383732
2² × 3 × 102031 × 4704465596881

2020-07-21

102031

4704465596881

2,697,448

4,377.2

8,175.5

exponent	prime factors	composite factor	digits	bits*
500807	24038737 16251472609991	390664875934277221367	21	68.404
500807	24038737 5769312617530563727343449	138686988683598810903348879183913	33	106.774
500807	16251472609991 5769312617530563727343449	93759825982273438439223794412885798959	38	126.140
500807	24038737 16251472609991 5769312617530563727343449	2253867797953637848726191278033431132210274783	46	150.659

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T18:48:29	alpertron	Manual testing	1500000	50000000	12	-	skipped known factor: 24038737 skipped known factor: 16251472609991	-	-	0.071	-	-	6.100%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-11-11T12:01:32	mognuts	Manual testing	1950000	72150000	2	7			-	-	0.115

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-11-11T12:01:32

mognuts

Manual testing

1950000

72150000

0.115

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-21T09:20:00	J Feitsma	Manual testing	?	?	16251472609991	43.886	14	2.26132e-6	0.012	4.72105e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-21T09:20:00

J Feitsma

Manual testing

16251472609991

43.886

2.26132e-6

0.012

4.72105e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.960 GHz-days
Estimated T-Level:	26.484

Digits	B1	Curves	Complete	FacMiss
20	11000	471 / 100	4.710	0.879%
25	50000	471 / 280	1.682	18.542%
30	250000	190 / 640	0.297	74.296%

New Calculation Method

Total ECM effort:	15.960 GHz-days
Estimated T-Level:	26.484

Digits	B1	Complete	FacMiss
20	11000	24.898	0.000%
25	50000	3.108	4.467%
30	250000	0.298	74.266%
35	1000000	0.023	97.739%
40	3000000	0.001	99.854%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	3.643
250000	25000000		144	9.335
250000	25000000	5769312617530563727343449	46	2.982

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-03-24T16:27:00	Richard B. Woods	Puttputt	50000	5000000						1	0.013
2015-05-29T10:16:00	TJAOI	Manual testing	50000	5000000						99	1.284
2016-02-26T13:30:32	TJAOI	Manual testing	50000	5000000						90	1.167
2016-09-09T13:48:12	TJAOI	Manual testing	50000	5000000						91	1.180
2018-03-16T09:30:30	TJAOI	Manual testing	250000	25000000						44	2.852
2020-07-20T18:00:27	nordi	sweet16	250000	25000000	5769312617530563727343449	82.255	46	2	6719378266810772	46	2.982
2020-09-04T07:38:01	TJAOI	Manual testing	250000	25000000						3	0.194
2020-09-04T07:38:44	TJAOI	Manual testing	250000	25000000						97	6.288

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T09:45:43

Oliver Kruse

GTX-0

24038737

16251472609991

702A18948E0073__

2017-11-03T03:31:40

kkmrkkblmbrbk

c4.xlarge

24038737

16251472609991

702A18948E0073__

2020-04-18T23:48:40

Oliver Kruse

AddPrpType5

24038737

16251472609991

0DCC2796B954F4__

2020-07-20T18:01:28

ATH

ec2-PRPCF

24038737

16251472609991

5769312617530563727343449

0DCC2796B954F468

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 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (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

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