M4695269 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	6.3285	65.6716%	-	-	-	-	6.3285	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0654	62.2951%	20000	400000	0.0078	3.1214%	0.0732	63.4720%	1.1769%
GPU72	2⁶⁵	1.5538	64.6154%	30000	600000	0.0117	2.2323%	1.5655	65.4053%	0.7899%
Difference	+2	+4.7746	+1.0563%	-30000	-600000	-0.0117	-2.2323%	+4.7630	+0.2664%	+0.2664%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.3285

65.6716%

6.3285

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0654

62.2951%

20000

400000

0.0078

3.1214%

0.0732

63.4720%

1.1769%

GPU72

2⁶⁵

1.5538

64.6154%

30000

600000

0.0117

2.2323%

1.5655

65.4053%

0.7899%

Difference

+4.7746

+1.0563%

-30000

-600000

-0.0117

-2.2323%

+4.7630

+0.2664%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4695269	34547789303	11	35.008	3679 13 × 283	-	13	283	1.751e-9	5.290e-6	5.471e-6
4695269	1647713670627319	16	50.549	175465311 3 × 7 × 829 × 10079	2014-06-03	829	10079	4.806e-5	0.0003	0.0003
4695269	5942124550734751391	19	62.366	632777861155 5 × 11 × 26251 × 438271	2016-08-01	26251	438271	0.1333	0.0093	0.0102
4695269	202347772062964626569	21	67.455	21548048904436 2² × 31² × 4021 × 1394089	2019-04-07	4021	1394089	9.1616	0.0152	0.0271

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4695269

34547789303

35.008

3679
13 × 283

283

1.751e-9

5.290e-6

5.471e-6

4695269

1647713670627319

50.549

175465311
3 × 7 × 829 × 10079

2014-06-03

829

10079

4.806e-5

0.0003

4695269

5942124550734751391

62.366

632777861155
5 × 11 × 26251 × 438271

2016-08-01

26251

438271

0.1333

0.0093

0.0102

4695269

202347772062964626569

67.455

21548048904436
2² × 31² × 4021 × 1394089

2019-04-07

4021

1394089

9.1616

0.0152

0.0271

exponent	prime factors	composite factor	digits	bits*
4695269	34547789303 1647713670627319	56924864724505356647768657	26	85.557
4695269	34547789303 5942124550734751391	205287266990967724896354170473	30	97.374
4695269	34547789303 202347772062964626569	6990668195162771568247887791407	31	102.463
4695269	1647713670627319 5942124550734751391	9790919854815866042044588477850729	34	112.915
4695269	1647713670627319 202347772062964626569	333411190249127517946953404804638511	36	118.005
4695269	5942124550734751391 202347772062964626569	1202375664161821560306251367905368307479	40	129.821
4695269	34547789303 1647713670627319 5942124550734751391	338254636226737889882028982064128467776951887	45	147.923
4695269	34547789303 1647713670627319 202347772062964626569	11518619551989305569610697359949119155107647833	47	153.013
4695269	34547789303 5942124550734751391 202347772062964626569	41539421108517299362143080412150200729398211097137	50	164.829
4695269	1647713670627319 5942124550734751391 202347772062964626569	19811708190690355762836695047436319284809392792094 18801	55	180.370
4695269	34547789303 1647713670627319 5942124550734751391 202347772062964626569	68445072030448975700859397809569354896143055069663 689150034885703	65	215.378

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-06-03T11:27:00	TJAOI	Manual testing	?	?	1647713670627319	50.549	16	1.61177e-5	1.322	3.44766e-5
2016-08-01T15:12:07	TJAOI	Manual testing	2⁶²	2⁶³*	5942124550734751391	62.366	19	0.002	1.257	0.005

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.591 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:	0.591 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	202347772062964626569	3	0.591

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-04-06T14:37:36	ATH	ec2-ECMCF	50000	5000000	202347772062964626569	67.455	3	2	8018853041152082	3	0.591

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-18T09:09:59

kkmrkkblmbrbk

c4.xlarge

34547789303

1647713670627319

5942124550734751391

307C9962270C5D__

2018-03-10T08:03:04

Oliver Kruse

GTX-4

34547789303

1647713670627319

5942124550734751391

307C9962270C5D__

2019-04-06T16:15:17

ATH

ec2-PRPCF

34547789303

1647713670627319

5942124550734751391

202347772062964626569

307C9962270C5D78

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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