M454627 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	unknown	3000000	100000000	0.1415	43.3373%	0.1415	43.3373%	43.3373%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	150000	0.0002	18.3797%	0.0002	61.2304%	8.7304%
GPU72	2⁴⁴	0.0000	56.8182%	8000	260000	0.0004	13.8555%	0.0004	62.8012%	5.9831%
Difference	-44	0.0000	-56.8182%	+2992000	+99740000	+0.1411	+29.4818%	+0.1411	-19.4639%	-19.4639%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

3000000

100000000

0.1415

43.3373%

0.1415

43.3373%

PrimeNet

2⁴⁰

0.0000

52.5000%

4500

150000

0.0002

18.3797%

0.0002

61.2304%

8.7304%

GPU72

2⁴⁴

0.0000

56.8182%

8000

260000

0.0004

13.8555%

0.0004

62.8012%

5.9831%

Difference

-44

0.0000

-56.8182%

+2992000

+99740000

+0.1411

+29.4818%

+0.1411

-19.4639%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
454627	2044462165271	13	40.895	2248505 5 × 7 × 17 × 3779	-	17	3779	5.443e-7	3.791e-6	6.568e-6
454627	487109931778471543535136079	27	88.654	535724815924341870957 3² × 13 × 127 × 2341 × 15401065499803	2020-08-03	2341	15401065499803	213,004,243	14,330	26,764

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

454627

2044462165271

40.895

2248505
5 × 7 × 17 × 3779

3779

5.443e-7

3.791e-6

6.568e-6

454627

487109931778471543535136079

88.654

535724815924341870957
3² × 13 × 127 × 2341 × 15401065499803

2020-08-03

2341

15401065499803

213,004,243

14,330

26,764

exponent	prime factors	composite factor	digits	bits*
454627	2044462165271 487109931778471543535136079	995877825848823023798701849939972912409	39	129.549

exponent

prime factors

composite factor

digits

bits*

454627

2044462165271
487109931778471543535136079

995877825848823023798701849939972912409

129.549

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T18:48:23	alpertron	Manual testing	3000000	100000000	12	-	skipped known factor: 2044462165271	-	-	0.141	-	-	34.826%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T18:48:23

alpertron

Manual testing

3000000

100000000

skipped known factor: 2044462165271

0.141

-

-

34.826%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.712 GHz-days
Estimated T-Level:	26.602

Digits	B1	Curves	Complete	FacMiss
20	11000	486 / 100	4.860	0.756%
25	50000	486 / 280	1.736	17.573%
30	250000	205 / 640	0.320	72.574%

New Calculation Method

Total ECM effort:	17.712 GHz-days
Estimated T-Level:	26.602

Digits	B1	Complete	FacMiss
20	11000	26.148	0.000%
25	50000	3.334	3.564%
30	250000	0.323	72.408%
35	1000000	0.025	97.543%
40	3000000	0.002	99.840%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	3.622
250000	25000000		44	2.835
250000	25000000	487109931778471543535136079	61	3.931
250000	35000000		100	7.324

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-01-30T08:16:00	Richard B. Woods	Puttputt	50000	5000000						1	0.013
2015-04-17T10:32:00	TJAOI	Manual testing	50000	5000000						99	1.276
2016-02-26T13:29:29	TJAOI	Manual testing	50000	5000000						90	1.160
2016-06-17T16:32:28	TJAOI	Manual testing	50000	5000000						91	1.173
2018-11-23T13:31:44	TJAOI	Manual testing	250000	25000000						44	2.835
2020-08-03T10:11:50	nordi	sweet16	250000	25000000	487109931778471543535136079	88.654	61	2	2154738754660450	61	3.931
2021-04-23T12:14:16	TJAOI	Manual testing	250000	35000000						59	4.321
2021-04-23T12:14:57	TJAOI	Manual testing	250000	35000000						41	3.003

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-25T02:42:15

Oliver Kruse

Doppelherz

2044462165271

FA71BA5B954A06__

2017-09-27T07:34:00

Oliver Kruse

Manual testing

2044462165271

FA71BA5B954A06__

2017-11-09T04:54:51

kkmrkkblmbrbk

c4.large

2044462165271

FA71BA5B954A06__

2020-04-18T19:36:02

Oliver Kruse

AddPrpType5

2044462165271

BE3DA8D62E661E__

2020-08-03T10:32:29

CrypticClue

cruncher

2044462165271

487109931778471543535136079

BE3DA8D62E661EAD

2020-08-03T22:47:37

atrench

Desktop

2044462165271

487109931778471543535136079

BE3DA8D62E661EAD

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 = 100000000 (P-1 stage 2)

B1 = 3000000 (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

10¹⁴

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