M5661911 Mersenne number exponent details

Residue

Status

L-L

02B383ED27A94CBF

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	2⁶⁷	5.2480	65.6716%	65000	1040000	0.0270	2.4274%	5.2751	66.5049%	0.8333%
PrimeNet	2⁶²	0.1085	62.9032%	24000	550000	0.0121	3.1765%	0.1206	64.0816%	1.1784%
GPU72	2⁶⁶	2.6084	65.1515%	36000	700000	0.0165	2.1940%	2.6249	65.9161%	0.7646%
Difference	+1	+2.6397	+0.5201%	+29000	+340000	+0.0105	+0.2334%	+2.6502	+0.5888%	+0.5888%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.2480

65.6716%

65000

1040000

0.0270

2.4274%

5.2751

66.5049%

0.8333%

PrimeNet

2⁶²

0.1085

62.9032%

24000

550000

0.0121

3.1765%

0.1206

64.0816%

1.1784%

GPU72

2⁶⁶

2.6084

65.1515%

36000

700000

0.0165

2.1940%

2.6249

65.9161%

0.7646%

Difference

+2.6397

+0.5201%

+29000

+340000

+0.0105

+0.2334%

+2.6502

+0.5888%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5661911	148792369226235918497	21	67.012	13139765816368 2⁴ × 269 × 467 × 6537301	2015-09-18	467	6537301	5.5543	0.0817	0.1523

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5661911

148792369226235918497

67.012

13139765816368
2⁴ × 269 × 467 × 6537301

2015-09-18

467

6537301

5.5543

0.0817

0.1523

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-08-24T00:00:00	ANONYMOUS	v4_computers	30000	292500		-		-	-	0.010	-	-	1.436%
2001-06-03T00:00:00	ANONYMOUS	v4_computers	20000	65000		-		-	-	0.005	-	-	0.750%
2011-05-22T03:24:00	harlee	P4_2600	65000	1040000		-		-	-	0.027	-	-	2.427%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.109	-	-
2009-04-10T04:58:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.173	-	-
2014-11-22T22:25:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.347	-	-
2014-11-23T20:01:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.660	-	-
2015-08-27T21:38:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.320	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.441 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.441 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.720
50000	5000000	148792369226235918497	3	0.720

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-05-21T16:53:00	sannerud.com	Jens2010	50000	5000000						3	0.720
2015-09-18T20:55:00	lopper	punani	50000	5000000	148792369226235918497	67.012	3	2		3	0.720

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	9E857AD00D06D6__	0.894
2000-05-10T00:00:00	ANONYMOUS	v4_computers	02B383ED27A94CBF	0.894
2001-07-17T00:00:00	ANONYMOUS	v4_computers	02B383ED27A94CBF	0.894

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:36:14

kkmrkkblmbrbk

Manual testing

148792369226235918497

5EE046924A4EE5__

2018-08-15T01:26:56

ATH

ec2-PRPCFDC

148792369226235918497

5EE046924A4EE5__

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 = 65000, B2 = 1040000 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 30000, B2 = 292500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000, B2 = 65000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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