M1448833 Mersenne number exponent details

Residue

Status

L-L

AFD32729A7BE9A41

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	20.5089	68.6567%	500000	15000000	0.0714	4.9277%	20.5803	70.2012%	1.5445%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9037%	0.0074	63.5889%	1.0889%
GPU72	2⁶⁰	0.1060	65.0000%	6500	90000	0.0006	1.3962%	0.1066	65.4887%	0.4887%
Difference	+7	+20.4029	+3.6567%	+493500	+14910000	+0.0708	+3.5314%	+20.4737	+4.7125%	+4.7125%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.5089

68.6567%

500000

15000000

0.0714

4.9277%

20.5803

70.2012%

1.5445%

PrimeNet

2⁵⁶

0.0066

62.5000%

7000

120000

0.0007

2.9037%

0.0074

63.5889%

1.0889%

GPU72

2⁶⁰

0.1060

65.0000%

6500

90000

0.0006

1.3962%

0.1066

65.4887%

0.4887%

Difference

+20.4029

+3.6567%

+493500

+14910000

+0.0708

+3.5314%

+20.4737

+4.7125%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1448833	625580901412216007	18	59.118	215891307491 190759 × 1131749	-	190759	1131749	0.0655	0.0134	0.0215
1448833	104487263157994464471583	24	76.468	36059112112298127 3 × 29 × 58657 × 7066037353	2018-09-22	58657	7066037353	16,386	21.316	39.807

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1448833

625580901412216007

59.118

215891307491
190759 × 1131749

190759

1131749

0.0655

0.0134

0.0215

1448833

104487263157994464471583

76.468

36059112112298127
3 × 29 × 58657 × 7066037353

2018-09-22

58657

7066037353

16,386

21.316

39.807

exponent	prime factors	composite factor	digits	bits*
1448833	625580901412216007 104487263157994464471583	65365236272473604838492070308862309229081	41	135.586

exponent

prime factors

composite factor

digits

bits*

1448833

625580901412216007
104487263157994464471583

65365236272473604838492070308862309229081

135.586

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:14:28	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 625580901412216007	-	-	0.071	-	-	4.928%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.434 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:	26.434 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.390	24.916%
30	250000	0.116	89.004%
35	1000000	0.008	99.198%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	11.79
50000	5000000	104487263157994464471583	2	0.095
250000	40000000		50	14.55

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-20T19:03:08	storm5510	HP-Z220-CMT	50000	5000000						3	0.142
2018-09-22T18:56:41	Chang Chia-Tche	exbpc13	50000	5000000	104487263157994464471583	76.468	2	2		2	0.095
2019-03-15T12:30:15	TJAOI	Manual testing	50000	5000000						246	11.64
2022-01-18T14:04:29	TJAOI	Manual testing	250000	40000000						50	14.55

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	ANONYMOUS	v4_computers	AFD32729A7BE9A41	0.055

date

userid

compid

res64

spent (GHz-days)

1999-01-02T00:00:00

ANONYMOUS

v4_computers

AFD32729A7BE9A41

0.055

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T01:29:26

Oliver Kruse

GTX-2

625580901412216007

ADF4DAB97E1888__

2017-10-27T11:49:19

Chang Chia-Tche

homura

625580901412216007

ADF4DAB97E1888__

2018-09-23T12:03:22

trebor

Laptop

625580901412216007

104487263157994464471583

8EE8220BF49D37__

2018-09-23T12:10:42

ANONYMOUS

625580901412216007

104487263157994464471583

8EE8220BF49D37__

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)

10³

10⁴

10⁵

10⁶

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