M1834109 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	16.2007	68.6567%	2000000	60000000	0.4059	7.4073%	16.6066	70.9784%	2.3217%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8803%	0.0117	64.2191%	1.0612%
GPU72	2⁶¹	0.1675	65.5738%	9000	140000	0.0013	1.5953%	0.1688	66.1230%	0.5492%
Difference	+6	+16.0333	+3.0829%	+1991000	+59860000	+0.4046	+5.8119%	+16.4379	+4.8554%	+4.8554%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.2007

68.6567%

2000000

60000000

0.4059

7.4073%

16.6066

70.9784%

2.3217%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8803%

0.0117

64.2191%

1.0612%

GPU72

2⁶¹

0.1675

65.5738%

9000

140000

0.0013

1.5953%

0.1688

66.1230%

0.5492%

Difference

+16.0333

+3.0829%

+1991000

+59860000

+0.4046

+5.8119%

+16.4379

+4.8554%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1834109	352300836243817	15	48.324	96041412 2² × 3² × 113 × 23609	-	113	23609	2.421e-5	0.0001	0.0002
1834109	1812307379629887877553	22	70.618	494056618126264 2³ × 251 × 246044132533	2021-02-26	251	246044132533	142.25	1,054.5	1,969.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1834109

352300836243817

48.324

96041412
2² × 3² × 113 × 23609

113

23609

2.421e-5

0.0001

0.0002

1834109

1812307379629887877553

70.618

494056618126264
2³ × 251 × 246044132533

2021-02-26

251

246044132533

142.25

1,054.5

1,969.5

exponent	prime factors	composite factor	digits	bits*
1834109	352300836243817 1812307379629887877553	638477405374450218227407906949339801	36	118.942

exponent

prime factors

composite factor

digits

bits*

1834109

352300836243817
1812307379629887877553

638477405374450218227407906949339801

118.942

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:39:53	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 352300836243817	-	-	0.101	-	-	5.070%
2021-02-26T19:19:23	riccardo uberti	Colab_noGPU14	2000000	60000000	12	-	skipped known factor: 352300836243817	-	-	0.406	-	-	7.407%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.838 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.838 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.652	0.002%
25	50000	0.980	37.513%
30	250000	0.062	93.966%
35	1000000	0.003	99.708%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.003
50000	6150000	1812307379629887877553	3	0.226
50000	6600000		219	17.06
50000	6750000		7	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-15T23:20:39	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2018-12-31T11:42:14	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-09T19:56:22	Greg Hogan	azure3	50000	5000000						3	0.207
2020-06-19T10:48:58	nordi	sweet16	50000	5000000						3	0.207
2020-07-16T11:41:19	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-09-04T18:43:21	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.484
2020-11-14T05:38:03	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2021-02-26T12:32:50	seatsea	dt	50000	6150000	1812307379629887877553	70.618	3	2	3727977481100242	3	0.226
2021-04-04T15:21:27	Deufo	Ryzen2600	50000	6750000						7	0.551
2021-04-30T08:12:29	TJAOI	Manual testing	50000	6600000						219	17.06

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T02:32:09

Oliver Kruse

GTX-0

352300836243817

2BC326AC25E2C0__

2017-11-06T09:29:12

ATH

ec2-1xf

352300836243817

2BC326AC25E2C0__

2021-02-26T13:02:46

riccardo uberti

Nomad2C

352300836243817

1812307379629887877553

BF2C11A1CBE366C8

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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