M1851749 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	16.0464	68.6567%	30000000	195066367860	838.2370	20.6994%	854.2834	75.1446%	6.4879%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0236%	0.0117	64.2719%	1.1140%
GPU72	2⁶¹	0.1659	65.5738%	9000	150000	0.0013	1.6313%	0.1672	66.1354%	0.5616%
Difference	+6	+15.8805	+3.0829%	+29991000	+195066217860	+838.2357	+19.0681%	+854.1162	+9.0092%	+9.0092%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0464

68.6567%

30000000

195066367860

838.2370

20.6994%

854.2834

75.1446%

6.4879%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0236%

0.0117

64.2719%

1.1140%

GPU72

2⁶¹

0.1659

65.5738%

9000

150000

0.0013

1.6313%

0.1672

66.1354%

0.5616%

Difference

+15.8805

+3.0829%

+29991000

+195066217860

+838.2357

+19.0681%

+854.1162

+9.0092%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1851749	14813993	8	23.820	4 2²	-	4	4	6.040e-13	3.146e-7	6.404e-7
1851749	766624087	9	29.514	207 3² × 23	2008-07-15	9	23	4.035e-11	7.680e-7	1.441e-6
1851749	814769561	9	29.602	220 2² × 5 × 11	2008-07-15	5	11	4.046e-11	4.190e-7	8.005e-7
1851749	304124230535387833	18	58.077	82118103084 2² × 3² × 17 × 23 × 5833909	2015-07-05	23	5833909	0.0246	0.0250	0.0467
1851749	3270824119699484839487	22	71.470	883171563667507 31 × 503 × 701 × 80797399	2021-05-25	701	80797399	389.38	0.3463	0.6467

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1851749

14813993

23.820

4
2²

6.040e-13

3.146e-7

6.404e-7

1851749

766624087

29.514

207
3² × 23

2008-07-15

4.035e-11

7.680e-7

1.441e-6

1851749

814769561

29.602

220
2² × 5 × 11

2008-07-15

4.046e-11

4.190e-7

8.005e-7

1851749

304124230535387833

58.077

82118103084
2² × 3² × 17 × 23 × 5833909

2015-07-05

5833909

0.0246

0.0250

0.0467

1851749

3270824119699484839487

71.470

883171563667507
31 × 503 × 701 × 80797399

2021-05-25

701

80797399

389.38

0.3463

0.6467

exponent	prime factors	composite factor	digits	bits*
1851749	14813993 766624087	11356763858449391	17	53.334
1851749	14813993 814769561	12069990573267073	17	53.422
1851749	766624087 814769561	624621970817015807	18	59.116
1851749	14813993 304124230535387833	4505294222281621610347169	25	81.898
1851749	14813993 766624087 814769561	9253145503329476445787351	25	82.936
1851749	766624087 304124230535387833	233148960568769218664533471	27	87.591
1851749	814769561 304124230535387833	247791165802780739658151313	27	87.679
1851749	14813993 3270824119699484839487	48453965613459330515766541591	29	95.291
1851749	766624087 3270824119699484839487	2507492554502196279442062923369	31	100.984
1851749	814769561 3270824119699484839487	2664967932115760714594978455207	31	101.072
1851749	14813993 766624087 304124230535387833	3453867069823023223911868187659703	34	111.412
1851749	14813993 814769561 304124230535387833	3670776595664233257830675943722809	34	111.500
1851749	766624087 814769561 304124230535387833	189962676250222406601614942436476231	36	117.193
1851749	14813993 766624087 3270824119699484839487	37145977149947654168280764052347902417	38	124.805
1851749	14813993 814769561 3270824119699484839487	39478816291587354415685008670587311551	38	124.892
1851749	304124230535387833 3270824119699484839487	994736868620193095775697269439297761671	39	129.548
1851749	766624087 814769561 3270824119699484839487	2043028607842523036136842933007736771009	40	130.586
1851749	14813993 766624087 814769561 304124230535387833	2814105756232060979839477545949361830700383	43	141.014
1851749	14813993 304124230535387833 3270824119699484839487	14736025008581460179469508919592870966309862303	47	153.368
1851749	14813993 766624087 814769561 3270824119699484839487	30265411495378881359669938251676081471569928937	47	154.406
1851749	766624087 304124230535387833 3270824119699484839487	762589243711194481812747475972294648462173969377	48	159.062
1851749	814769561 304124230535387833 3270824119699484839487	810481321756189404380395818689955353424963296431	48	159.149
1851749	14813993 766624087 304124230535387833 3270824119699484839487	11296991718212929075212668419821241116256105947133 092361	56	182.882
1851749	14813993 814769561 304124230535387833 3270824119699484839487	12006464627126937543165352995302267775949932298585 758983	56	182.970
1851749	766624087 814769561 304124230535387833 3270824119699484839487	62133450332189193873219474520180455889017481013492 5733497	57	188.663
1851749	14813993 766624087 814769561 304124230535387833 3270824119699484839487	92044449828689839271351618300563163227671374061151 18871544423521	64	212.484

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-07-05T16:35:00	alpertron	Manual testing	500000	15000000	12		304124230535387833	18	58.077	0.101	0.201	0.203	5.076%
2021-12-26T19:52:42	mikr	Nitron	30000000	195066367860		-	skipped known factor: 14813993 skipped known factor: 766624087 skipped known factor: 814769561 skipped known factor: 304124230535387833 skipped known factor: 3270824119699484839487	-	-	838.2	-	-	20.699%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-07-05T16:35:00

alpertron

Manual testing

500000

15000000

304124230535387833

58.077

0.101

0.201

0.203

5.076%

2021-12-26T19:52:42

mikr

Nitron

30000000

195066367860

skipped known factor: 14813993
skipped known factor: 766624087
skipped known factor: 814769561
skipped known factor: 304124230535387833
skipped known factor: 3270824119699484839487

838.2

-

-

20.699%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-05-25T11:11:08	mikr	Nitron	5000000	425000000	195	43			-	-	2.362

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-05-25T11:11:08

mikr

Nitron

5000000

425000000

195

2.362

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	766624087	29.514	9	1.73053e-12	0.215	3.69852e-12
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	814769561	29.602	9	1.83921e-12	0.215	3.93079e-12

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:47:00

J Feitsma

Manual testing

766624087

29.514

1.73053e-12

0.215

3.69852e-12

2008-07-15T07:47:00

J Feitsma

Manual testing

814769561

29.602

1.83921e-12

0.215

3.93079e-12

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.491 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	19.491 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.679	0.017%
25	50000	0.786	45.557%
30	250000	0.049	95.253%
35	1000000	0.002	99.777%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.282
50000	5000000	3270824119699484839487	3	0.207
50000	6600000		218	17.00

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-17T13:34:46	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-01-15T05:04:31	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-18T05:04:59	nordi	sweet16	50000	5000000						3	0.207
2020-07-15T02:59:51	argusdusty	Argus-PC	50000	5000000						3	0.207
2020-08-31T20:10:31	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.484
2020-11-11T12:57:48	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.484
2021-02-10T01:31:17	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-05-25T01:51:24	Chang Chia-Tche	exbpc13	50000	5000000	3270824119699484839487	71.470	3	2	7947068952706309	3	0.207
2021-10-07T10:31:06	TJAOI	Manual testing	50000	6600000						218	17.00

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:47

alpertron

Manual testing

14813993

766624087

814769561

304124230535387833

0904F58026E364__

2017-10-20T01:06:59

Oliver Kruse

Threadripper

14813993

766624087

814769561

304124230535387833

0904F58026E364__

2021-05-25T05:57:57

mikr

Nitron

14813993

766624087

814769561

304124230535387833

3270824119699484839487

74D4A5FCDF40B20E

2021-05-26T22:32:13

kutens

sol

14813993

766624087

814769561

304124230535387833

3270824119699484839487

74D4A5FCDF40B20E

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