M291877 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	101.8029	71.6418%	50000	50000	0.0005	0.3966%	101.8034	71.7543%	0.1125%
PrimeNet	2⁴⁰	0.0000	52.5000%	3000	80000	0.0001	15.0975%	0.0001	59.6713%	7.1713%
GPU72	2⁴⁴	0.0000	56.8182%	5500	140000	0.0001	11.1988%	0.0001	61.6540%	4.8358%
Difference	+23	+101.8029	+14.8236%	+44500	-90000	+0.0004	-10.8021%	+101.8032	+10.1003%	+10.1003%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

101.8029

71.6418%

50000

0.0005

0.3966%

101.8034

71.7543%

0.1125%

PrimeNet

2⁴⁰

0.0000

52.5000%

3000

80000

0.0001

15.0975%

0.0001

59.6713%

7.1713%

GPU72

2⁴⁴

0.0000

56.8182%

5500

140000

0.0001

11.1988%

0.0001

61.6540%

4.8358%

Difference

+23

+101.8029

+14.8236%

+44500

-90000

+0.0004

-10.8021%

+101.8032

+10.1003%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
291877	10130536966481	14	43.204	17354120 2³ × 5 × 7 × 61979	-	8	61979	5.231e-6	3.353e-5	6.249e-5
291877	232919405790689	15	47.727	399002672 2⁴ × 37 × 673991	2014-03-13	37	673991	7.803e-5	0.0004	0.0007
291877	89814933379384088399	20	66.284	153857503981787 701581 × 219301127	2014-09-15	701581	219301127	68.409	0.1250	0.2211
291877	16800751130359935394857079	26	83.797	28780532776409130207 3³ × 198941 × 5358099428401	2020-06-28	198941	5358099428401	8,319,651	2,892.5	5,402.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

291877

10130536966481

43.204

17354120
2³ × 5 × 7 × 61979

61979

5.231e-6

3.353e-5

6.249e-5

291877

232919405790689

47.727

399002672
2⁴ × 37 × 673991

2014-03-13

673991

7.803e-5

0.0004

0.0007

291877

89814933379384088399

66.284

153857503981787
701581 × 219301127

2014-09-15

701581

219301127

68.409

0.1250

0.2211

291877

16800751130359935394857079

83.797

28780532776409130207
3³ × 198941 × 5358099428401

2020-06-28

198941

5358099428401

8,319,651

2,892.5

5,402.3

exponent	prime factors	composite factor	digits	bits*
291877	10130536966481 232919405790689	2359598650573363607294895409	28	90.931
291877	10130536966481 89814933379384088399	909873502741878792793765003953919	33	109.487
291877	232919405790689 89814933379384088399	20919640913856460995174308067116911	35	114.010
291877	10130536966481 16800751130359935394857079	170200630390758771696674574021208568999	39	127.0005
291877	232919405790689 16800751130359935394857079	3913220970120682698521717858142143937431	40	131.524
291877	89814933379384088399 16800751130359935394857079	1508958343496889515383489997491094029306926521	46	150.080
291877	10130536966481 232919405790689 89814933379384088399	211927195603331247009115433226078718109515260191	48	157.214
291877	10130536966481 232919405790689 16800751130359935394857079	39643029695816216845158944693720279530403907808250 311	53	174.727
291877	10130536966481 89814933379384088399 16800751130359935394857079	15286558279675173904832274942574234008468922708932 906942601	59	193.284
291877	232919405790689 89814933379384088399 16800751130359935394857079	35146568073019788893507291106813343673145753458870 4428962969	60	197.807
291877	10130536966481 232919405790689 89814933379384088399 16800751130359935394857079	35605360710866785787831436840587263956524249522779 24897794445329943242089	73	241.011

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-02-06T16:49:09	Lisander Viaene	Manual testing	50000	50000		-		-	-	0.000	-	-	0.397%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-02-06T16:49:09

Lisander Viaene

Manual testing

50000

0.000

-

-

0.397%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-03-13T11:34:00	TJAOI	Manual testing	?	?	232919405790689	47.727	15	1.37925e-5	0.004	2.86506e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-03-13T11:34:00

TJAOI

Manual testing

232919405790689

47.727

1.37925e-5

0.004

2.86506e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.843 GHz-days
Estimated T-Level:	27.953

Digits	B1	Curves	Complete	FacMiss
20	11000	616 / 100	6.160	0.205%
25	50000	616 / 280	2.200	11.037%
30	250000	378 / 640	0.591	55.373%

New Calculation Method

Total ECM effort:	16.843 GHz-days
Estimated T-Level:	27.953

Digits	B1	Complete	FacMiss
20	11000	39.177	0.000%
25	50000	5.347	0.476%
30	250000	0.547	57.862%
35	1000000	0.044	95.724%
40	3000000	0.003	99.713%

ECM Summary

B1	B2	factor	curves	GHz-days
		89814933379384088399	1	0.00000e+0
50000	5000000		238	1.742
250000	25000000		155	5.674
250000	25000000	16800751130359935394857079	3	0.110
250000	36750000		220	9.318

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-09-15T12:12:00	TJAOI	Manual testing	50000	5000000						7	0.051
2014-09-15T12:12:00	TJAOI	Manual testing			89814933379384088399	66.284		1		1	-
2015-01-16T11:45:00	TJAOI	Manual testing	50000	5000000						50	0.366
2015-10-30T13:18:28	TJAOI	Manual testing	50000	5000000						90	0.659
2016-04-08T13:16:49	TJAOI	Manual testing	50000	5000000						91	0.666
2017-09-08T12:45:39	TJAOI	Manual testing	250000	25000000						44	1.611
2020-06-19T14:06:07	kracker	O0	250000	25000000						3	0.110
2020-06-28T15:08:08	nordi	sweet16	250000	25000000	16800751130359935394857079	83.797	3	2	2423879145108621	3	0.110
2020-07-12T16:19:27	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						3	0.110
2020-07-24T05:36:59	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						3	0.110
2020-08-08T11:58:21	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.110
2020-09-20T16:49:31	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						7	0.256
2020-10-25T22:14:46	nordi	sweet16	250000	25000000						7	0.256
2020-11-09T07:50:51	nordi	sweet16	250000	25000000						7	0.256
2020-12-18T11:08:55	TJAOI	Manual testing	250000	25000000						78	2.855
2022-04-05T09:13:43	nordi	sweet16_ccx2	250000	36750000						220	9.318

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T13:20:04

Oliver Kruse

Ollaptop

FFF09432AD575E__

2017-09-22T20:36:41

Oliver Kruse

Manual testing

FFF09432AD575E__

2017-10-12T20:23:28

Oliver Kruse

GTX-2

FFF09432AD575E__

2017-11-06T18:06:53

kkmrkkblmbrbk

c4.xlarge

10130536966481

232919405790689

89814933379384088399

FFF09432AD575E__

2020-04-17T22:12:43

Oliver Kruse

AddPrpType5

10130536966481

232919405790689

89814933379384088399

680AA2BFA71941__

2020-06-30T02:47:27

mnd9

mnd

10130536966481

232919405790689

89814933379384088399

16800751130359935394857079

680AA2BFA719415F

2020-07-01T04:26:27

fre_games

gpu

10130536966481

232919405790689

89814933379384088399

16800751130359935394857079

680AA2BFA719415F

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