M1234841 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	24.0630	68.6567%	300000	10000000	0.0368	4.1766%	24.0998	69.9658%	1.3091%
PrimeNet	2⁵⁶	0.0078	62.5000%	5500	90000	0.0004	2.4304%	0.0082	63.4114%	0.9114%
GPU72	2⁶⁰	0.1244	65.0000%	5000	30000	0.0003	0.8313%	0.1247	65.2909%	0.2909%
Difference	+7	+23.9386	+3.6567%	+295000	+9970000	+0.0366	+3.3453%	+23.9751	+4.6749%	+4.6749%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

24.0630

68.6567%

300000

10000000

0.0368

4.1766%

24.0998

69.9658%

1.3091%

PrimeNet

2⁵⁶

0.0078

62.5000%

5500

90000

0.0004

2.4304%

0.0082

63.4114%

0.9114%

GPU72

2⁶⁰

0.1244

65.0000%

5000

30000

0.0003

0.8313%

0.1247

65.2909%

0.2909%

Difference

+23.9386

+3.6567%

+295000

+9970000

+0.0366

+3.3453%

+23.9751

+4.6749%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1234841	2283984842127689	16	51.020	924809284 2² × 7 × 41 × 805583	-	41	805583	0.0003	0.0020	0.0036
1234841	252296355622611007	18	57.808	102157425783 3² × 7 × 1621546441	2015-07-17	9	1621546441	0.0299	3.9285	7.3373

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1234841

2283984842127689

51.020

924809284
2² × 7 × 41 × 805583

805583

0.0003

0.0020

0.0036

1234841

252296355622611007

57.808

102157425783
3² × 7 × 1621546441

2015-07-17

1621546441

0.0299

3.9285

7.3373

exponent	prime factors	composite factor	digits	bits*
1234841	2283984842127689 252296355622611007	576241051966100481803451470872823	33	108.828

exponent

prime factors

composite factor

digits

bits*

1234841

2283984842127689
252296355622611007

576241051966100481803451470872823

108.828

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:02:38	alpertron	Manual testing	300000	10000000	12	-	skipped known factor: 2283984842127689	-	-	0.037	-	-	4.177%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-07-17T10:45:00	TJAOI	Manual testing	2⁵⁷	2⁵⁸*	252296355622611007	57.808	18	0.014	0.077	0.029

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.775 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	19.775 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	15.208	0.000%
25	50000	1.667	18.888%
30	250000	0.137	87.162%
35	1000000	0.009	99.076%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	10.41
250000	35000000		44	9.369

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-10-23T20:55:46	Oliver Kruse	ECM-HTC	50000	5000000						3	0.111
2018-01-05T12:41:00	TJAOI	Manual testing	50000	5000000						140	5.185
2018-09-28T10:42:52	TJAOI	Manual testing	50000	5000000						138	5.111
2021-05-14T12:05:23	TJAOI	Manual testing	250000	35000000						44	9.369

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T17:02:24

Oliver Kruse

GTX-2

2283984842127689

252296355622611007

AA23319E37E71C__

2017-10-20T02:07:50

kkmrkkblmbrbk

c4.xlarge

2283984842127689

252296355622611007

AA23319E37E71C__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (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