M1865011 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	15.9323	68.6567%	500000	15000000	0.1015	5.0802%	16.0338	70.2490%	1.5923%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0276%	0.0116	64.2733%	1.1154%
GPU72	2⁶¹	0.1647	65.5738%	10000	150000	0.0014	1.6887%	0.1661	66.1551%	0.5814%
Difference	+6	+15.7676	+3.0829%	+490000	+14850000	+0.1001	+3.3914%	+15.8677	+4.0939%	+4.0939%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9323

68.6567%

500000

15000000

0.1015

5.0802%

16.0338

70.2490%

1.5923%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0276%

0.0116

64.2733%

1.1154%

GPU72

2⁶¹

0.1647

65.5738%

10000

150000

0.0014

1.6887%

0.1661

66.1551%

0.5814%

Difference

+15.7676

+3.0829%

+490000

+14850000

+0.1001

+3.3914%

+15.8677

+4.0939%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1865011	18650111	8	24.153	5 5	-	1	5	1.200e-12	9.581e-8	1.601e-7
1865011	242451431	9	27.853	65 5 × 13	2008-07-15	5	13	9.722e-12	4.276e-7	8.005e-7
1865011	13916219719097	14	43.662	3730868 2² × 229 × 4073	2008-09-30	229	4073	9.721e-7	3.449e-5	3.666e-5
1865011	57210331431601	14	45.701	15337800 2³ × 3² × 5² × 8521	2014-01-28	25	8521	4.700e-6	3.838e-5	6.820e-5
1865011	3429902397420139941799	22	71.539	919539455107809 3 × 8849 × 34638168347	2020-07-03	8849	34638168347	410.04	148.45	277.26

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1865011

18650111

24.153

5
5

1.200e-12

9.581e-8

1.601e-7

1865011

242451431

27.853

65
5 × 13

2008-07-15

9.722e-12

4.276e-7

8.005e-7

1865011

13916219719097

43.662

3730868
2² × 229 × 4073

2008-09-30

229

4073

9.721e-7

3.449e-5

3.666e-5

1865011

57210331431601

45.701

15337800
2³ × 3² × 5² × 8521

2014-01-28

8521

4.700e-6

3.838e-5

6.820e-5

1865011

3429902397420139941799

71.539

919539455107809
3 × 8849 × 34638168347

2020-07-03

8849

34638168347

410.04

148.45

277.26

exponent	prime factors	composite factor	digits	bits*
1865011	18650111 242451431	4521746100258841	16	52.006
1865011	18650111 13916219719097	259539042461547869767	21	67.815
1865011	18650111 57210331431601	1066979031546147557711	22	69.854
1865011	242451431 13916219719097	3374007385005485677807	22	71.515
1865011	242451431 57210331431601	13870726723575941071031	23	73.554
1865011	13916219719097 57210331431601	796151542404520738088984297	27	89.363
1865011	18650111 242451431 13916219719097	62925612245172043500010786577	29	95.668
1865011	18650111 3429902397420139941799	63968060431051723550084889689	29	95.691
1865011	18650111 242451431 57210331431601	258690593045357617904187034441	30	97.707
1865011	242451431 3429902397420139941799	831584744444843637109424264369	30	99.392
1865011	18650111 13916219719097 57210331431601	14848314638665518667161485016306967	35	113.516
1865011	13916219719097 3429902397420139941799	47731275377556226718352509708835503	35	115.200
1865011	242451431 13916219719097 57210331431601	193028080748833233818850448144179007	36	117.216
1865011	57210331431601 3429902397420139941799	196225852934449056765571344489390199	36	117.240
1865011	18650111 242451431 3429902397420139941799	15509147789802967209734481676575194959	38	123.544
1865011	18650111 13916219719097 3429902397420139941799	890193583962990537038440043198359811690833	42	139.353
1865011	18650111 242451431 13916219719097 57210331431601	3599995132082702931210514750288682484419777	43	141.369
1865011	18650111 57210331431601 3429902397420139941799	3659633938297150632523206553146365533662089	43	141.393
1865011	242451431 13916219719097 3429902397420139941799	11572516018743572450824999941348561045954793	44	143.054
1865011	242451431 57210331431601 3429902397420139941799	47575238843152723009413004004046618064924769	44	145.093
1865011	13916219719097 57210331431601 3429902397420139941799	2730722084003007885896635862990854294024604930303	49	160.902
1865011	18650111 242451431 13916219719097 3429902397420139941799	21582870829884570674442829048114415319733299043202 3	51	167.206
1865011	18650111 242451431 57210331431601 3429902397420139941799	88728348527630987407780656951891387608545214849935 9	51	169.246
1865011	18650111 13916219719097 57210331431601 3429902397420139941799	50928269976807421405847593371360224568385518681298 213633	56	185.055
1865011	242451431 13916219719097 57210331431601 3429902397420139941799	66206747692983147023992408306805256349876021456161 7613593	57	188.755
1865011	18650111 242451431 13916219719097 57210331431601 3429902397420139941799	12347631934231296131267780780792400863086426363957 984833064558823	65	212.908

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:25	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 18650111 skipped known factor: 242451431 skipped known factor: 13916219719097 skipped known factor: 57210331431601	-	-	0.101	-	-	5.080%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:25

alpertron

Manual testing

500000

15000000

skipped known factor: 18650111
skipped known factor: 242451431
skipped known factor: 13916219719097
skipped known factor: 57210331431601

0.101

-

-

5.080%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-09-30T13:30:00	markr	Manual testing	?	?	13916219719097	43.662	14	3.43801e-7	0.216	7.34186e-7
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	242451431	27.853	9	1.34885e-13	0.216	2.88048e-13
2014-01-28T11:29:00	TJAOI	Manual testing	?	?	57210331431601	45.701	14	2.18684e-6	0.216	4.66990e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-09-30T13:30:00

markr

Manual testing

13916219719097

43.662

3.43801e-7

0.216

7.34186e-7

2008-07-15T07:47:00

J Feitsma

Manual testing

242451431

27.853

1.34885e-13

0.216

2.88048e-13

2014-01-28T11:29:00

TJAOI

Manual testing

57210331431601

45.701

2.18684e-6

0.216

4.66990e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.239 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.239 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.566	0.019%
25	50000	0.776	46.025%
30	250000	0.048	95.313%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		37	2.561
50000	5000000	3429902397420139941799	3	0.208
50000	6600000		211	16.47

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T17:57:30	Oliver Kruse	ECM-HTC	50000	5000000						3	0.208
2019-01-18T14:16:04	tottenhoff	2018pc	50000	5000000						3	0.208
2020-07-03T11:34:25	nordi	sweet16	50000	5000000	3429902397420139941799	71.539	3	2	7196587617965843	3	0.208
2020-08-03T01:10:34	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.208
2020-10-10T17:26:31	nordi	sweet16	50000	5000000						7	0.485
2020-12-07T08:41:28	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.485
2021-05-13T15:57:58	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.485
2021-07-10T03:05:49	rushyn	linux	50000	5000000						7	0.485
2021-08-20T12:36:53	TJAOI	Manual testing	50000	6600000						211	16.47

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T09:58:56

Oliver Kruse

GTX-3

18650111

242451431

13916219719097

57210331431601

1502D0B5A8E77CBE

2017-10-05T21:45:30

Oliver Kruse

Manual testing

18650111

242451431

13916219719097

57210331431601

1502D0B5A8E77C__

2017-11-11T05:07:51

kkmrkkblmbrbk

c4.xlarge

18650111

242451431

13916219719097

57210331431601

1502D0B5A8E77C__

2020-07-03T13:38:06

CrypticClue

cruncher

18650111

242451431

13916219719097

57210331431601

3429902397420139941799

A6FEB5C6394BDB45

2020-07-04T14:30:22

marssystems

SYSTEM01

18650111

242451431

13916219719097

57210331431601

3429902397420139941799

A6FEB5C6394BDB45

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