M35821609 Mersenne number exponent details

Residue

Status

L-L

ECCE249D7AB17988

double-checked

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	2⁷²	26.6971	63.8889%	1200000	73200000	9.2850	6.5083%	35.9821	66.2391%	2.3502%
PrimeNet	2⁶⁷	0.8295	61.1940%	160000	6000000	0.8667	5.3528%	1.6962	63.2712%	2.0772%
GPU72	2⁷¹	13.3461	63.3803%	260000	8000000	1.2356	4.0175%	14.5817	64.8515%	1.4712%
Difference	+1	+13.3510	+0.5086%	+940000	+65200000	+8.0494	+2.4908%	+21.4005	+1.3876%	+1.3876%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

26.6971

63.8889%

1200000

73200000

9.2850

6.5083%

35.9821

66.2391%

2.3502%

PrimeNet

2⁶⁷

0.8295

61.1940%

160000

6000000

0.8667

5.3528%

1.6962

63.2712%

2.0772%

GPU72

2⁷¹

13.3461

63.3803%

260000

8000000

1.2356

4.0175%

14.5817

64.8515%

1.4712%

Difference

+13.3510

+0.5086%

+940000

+65200000

+8.0494

+2.4908%

+21.4005

+1.3876%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
35821609	37533512686961073352872057770174521	35	114.854	523894846361606388937918140 2² × 3 × 5 × 23 × 117101 × 173777 × 971063 × 19211653	2021-06-30	971063	19211653	4.282e+9	3.5613	3.5820

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

35821609

37533512686961073352872057770174521

114.854

523894846361606388937918140
2² × 3 × 5 × 23 × 117101 × 173777 × 971063 × 19211653

2021-06-30

971063

19211653

4.282e+9

3.5613

3.5820

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2007-03-20T00:00:00	ANONYMOUS	v4_computers	485000	485000		-		-	-	0.879	-	-	1.714%
2021-06-30T05:36:17	firejuggler	Maison	1200000	73200000			37533512686961073352872057770174521	35	114.854	9.285	89.55	18.57	6.508%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2004-08-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.004	-	-
2006-04-28T00:00:00	TMarshall	v4_computers	2¹	2⁶⁹		-	-	3.333	-	-
2014-09-19T17:26:00	LaurV	Manual testing	2⁶⁹	2⁷⁰		-	-	3.338	-	-
2014-10-03T00:45:00	monst	Manual testing	2⁷⁰	2⁷¹		-	-	6.676	-	-
2021-07-04T18:58:56	firejuggler	Manual testing	2⁷¹	2⁷²		-	-	13.35	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2007-08-14T00:00:00	2knarf	v4_computers	ECCE249D7AB17988	44.78
2007-12-03T00:00:00	2knarf	v4_computers	ECCE249D7AB17988	44.78
2014-10-28T10:58:00	vwflat4	DC1	ECCE249D7AB17988	44.78

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 = 1200000, B2 = 73200000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 485000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

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