M1966831 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	15.1075	68.6567%	500000	1964033610	10.2468	10.0566%	25.3543	71.8088%	3.1521%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0014	2.4709%	0.0210	64.6877%	0.8946%
GPU72	2⁶²	0.3124	66.1290%	8000	100000	0.0012	1.1955%	0.3136	66.5340%	0.4049%
Difference	+5	+14.7951	+2.5277%	+492000	+1963933610	+10.2455	+8.8612%	+25.0407	+5.2748%	+5.2748%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.1075

68.6567%

500000

1964033610

10.2468

10.0566%

25.3543

71.8088%

3.1521%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0014

2.4709%

0.0210

64.6877%

0.8946%

GPU72

2⁶²

0.3124

66.1290%

8000

100000

0.0012

1.1955%

0.3136

66.5340%

0.4049%

Difference

+14.7951

+2.5277%

+492000

+1963933610

+10.2455

+8.8612%

+25.0407

+5.2748%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1966831	18334798583	11	34.094	4661 59 × 79	-	59	79	1.174e-9	5.729e-6	1.145e-5
1966831	758521104480233	15	49.430	192828236 2² × 48207059	2008-08-26	4	48207059	6.533e-5	0.2504	0.4677
1966831	149355313360148992079	21	67.017	37968517213769 19 × 113 × 17684451427	2021-01-21	113	17684451427	18.361	91.857	171.56

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1966831

18334798583

34.094

4661
59 × 79

1.174e-9

5.729e-6

1.145e-5

1966831

758521104480233

49.430

192828236
2² × 48207059

2008-08-26

48207059

6.533e-5

0.2504

0.4677

1966831

149355313360148992079

67.017

37968517213769
19 × 113 × 17684451427

2021-01-21

113

17684451427

18.361

91.857

171.56

exponent	prime factors	composite factor	digits	bits*
1966831	18334798583 758521104480233	13907331671599770959909839	26	83.524
1966831	18334798583 149355313360148992079	2738399587759180708638927424057	31	101.111
1966831	758521104480233 149355313360148992079	113289157249931513277134766129074407	36	116.447
1966831	18334798583 758521104480233 149355313360148992079	2077133879815308486480656196323389832565165281	46	150.541

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-12T02:29:06	Lisander Viaene	Desktop	500000	1964033610		-	skipped known factor: 18334798583 skipped known factor: 758521104480233	-	-	10.25	-	-	10.057%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	758521104480233	49.430	15	2.72027e-5	0.282	5.93669e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T20:20:00

ANONYMOUS

Manual testing

758521104480233

49.430

2.72027e-5

0.282

5.93669e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.937 GHz-days
Estimated T-Level:	2.250

Digits	B1	Curves	Complete	FacMiss
20	11000	45 / 100	0.450	63.619%
25	50000	45 / 280	0.161	85.129%

New Calculation Method

Total ECM effort:	3.937 GHz-days
Estimated T-Level:	2.250

Digits	B1	Complete	FacMiss
20	11000	1.485	22.657%
25	50000	0.134	87.465%
30	250000	0.008	99.177%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		34	2.870
50000	6750000	149355313360148992079	4	0.385
50000	6900000		7	0.681

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-21T19:18:21	Oliver Kruse	HTC5	50000	5000000						3	0.253
2019-03-21T09:45:41	MarkS	laptop64	50000	5000000						3	0.253
2021-01-21T18:53:20	nordi	sweet16	50000	6750000	149355313360148992079	67.017	4	2	1082639147727478	4	0.385
2021-03-20T00:21:04	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.591
2021-07-12T03:56:24	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.591
2021-09-24T17:12:04	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.591
2022-01-28T06:12:20	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.591
2022-05-23T01:20:48	MarkS	desktop-i7	50000	6900000						7	0.681

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T09:49:36

Oliver Kruse

GTX-3

18334798583

758521104480233

AB1A4A28832493__

2017-11-12T05:01:58

kkmrkkblmbrbk

old

18334798583

758521104480233

AB1A4A28832493__

2021-01-23T16:20:43

marcomich

sisg6

18334798583

758521104480233

149355313360148992079

8BB6E4F9846F9F__

2021-01-24T04:35:09

Oliver Kruse

IOS-5

18334798583

758521104480233

149355313360148992079

8BB6E4F9846F9F88

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 = 1964033610 (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

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