M1846283 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	16.0939	68.6567%	500000	2835864570	12.1910	10.3816%	28.2849	71.9107%	3.2539%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0220%	0.0118	64.2713%	1.1134%
GPU72	2⁶¹	0.1664	65.5738%	9000	150000	0.0013	1.6303%	0.1677	66.1350%	0.5612%
Difference	+6	+15.9275	+3.0829%	+491000	+2835714570	+12.1897	+8.7513%	+28.1172	+5.7756%	+5.7756%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0939

68.6567%

500000

2835864570

12.1910

10.3816%

28.2849

71.9107%

3.2539%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0220%

0.0118

64.2713%

1.1134%

GPU72

2⁶¹

0.1664

65.5738%

9000

150000

0.0013

1.6303%

0.1677

66.1350%

0.5612%

Difference

+15.9275

+3.0829%

+491000

+2835714570

+12.1897

+8.7513%

+28.1172

+5.7756%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1846283	3692567	7	21.816	1 1	-	1	1	1.514e-13	7.866e-8	1.601e-7
1846283	72108428849	11	36.069	19528 2³ × 2441	2008-07-15	8	2441	6.083e-9	1.106e-5	1.954e-5
1846283	1809713718432634665013457	25	80.582	490096512406991416 2³ × 109 × 562037284870403	2021-04-13	109	562037284870403	196,816	2,408,751	4,498,877

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1846283

3692567

21.816

1
1

1.514e-13

7.866e-8

1.601e-7

1846283

72108428849

36.069

19528
2³ × 2441

2008-07-15

2441

6.083e-9

1.106e-5

1.954e-5

1846283

1809713718432634665013457

80.582

490096512406991416
2³ × 109 × 562037284870403

2021-04-13

109

562037284870403

196,816

2,408,751

4,498,877

exponent	prime factors	composite factor	digits	bits*
1846283	3692567 72108428849	266265204789665383	18	57.886
1846283	3692567 1809713718432634665013457	6682489156131638487084745874119	31	102.398
1846283	72108428849 1809713718432634665013457	130495612902658856541733813712020993	36	116.651
1846283	3692567 72108428849 1809713718432634665013457	481863793849132305923740403297156222059031	42	138.468

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-04-11T13:44:05	Lisander Viaene	Desktop	500000	2835864570		-	skipped known factor: 3692567 skipped known factor: 72108428849	-	-	12.19	-	-	10.382%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-04-11T13:44:05

Lisander Viaene

Desktop

500000

2835864570

skipped known factor: 3692567
skipped known factor: 72108428849

12.19

-

-

10.382%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	72108428849	36.069	11	1.12477e-9	0.214	2.40384e-9

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:47:00

J Feitsma

Manual testing

72108428849

36.069

1.12477e-9

0.214

2.40384e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.892 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:	19.892 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.841	0.014%
25	50000	0.802	44.846%
30	250000	0.050	95.154%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.005
50000	5000000	1809713718432634665013457	1	0.069
50000	6600000		220	17.15
50000	6750000		7	0.551
84000	8400000		1	0.116

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-17T02:27:05	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-01-13T19:26:56	tottenhoff	i7-8700k-01	50000	5000000						3	0.207
2020-06-07T19:03:05	-Anonymous-	aws-nano	50000	5000000						3	0.207
2020-07-03T11:33:57	nordi	sweet16	50000	5000000						3	0.207
2020-08-02T18:37:22	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-10-10T13:06:10	nordi	sweet16	50000	5000000						7	0.484
2021-01-10T14:30:25	Poao	hosthatch-US	50000	5000000						7	0.484
2021-02-05T21:27:52	Peredron	Peredron	84000	8400000						1	0.116
2021-04-13T05:15:55	Chang Chia-Tche	exbpc13	50000	5000000	1809713718432634665013457	80.582	1	2	1750815193550758	1	0.069
2021-04-25T21:36:59	nordi	sweet16	50000	6750000						7	0.551
2021-07-09T11:24:35	TJAOI	Manual testing	50000	6600000						220	17.15

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T05:20:05

Oliver Kruse

GTX-0

3692567

72108428849

782630ED49CE8A__

2017-11-06T19:07:56

kkmrkkblmbrbk

c4.xlarge

3692567

72108428849

782630ED49CE8A__

2021-04-13T05:26:57

SRJ2877

LTOS

3692567

72108428849

1809713718432634665013457

C9AA81A5701376B2

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 = 2835864570 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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