M1986631 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	14.9569	68.6567%	-	-	-	-	14.9569	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0193	63.7931%	8000	140000	0.0014	2.4756%	0.0208	64.6895%	0.8964%
GPU72	2⁶²	0.3092	66.1290%	8000	100000	0.0012	1.1980%	0.3105	66.5348%	0.4058%
Difference	+5	+14.6477	+2.5277%	-8000	-100000	-0.0012	-1.1980%	+14.6465	+2.1219%	+2.1219%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.9569

68.6567%

14.9569

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0193

63.7931%

8000

140000

0.0014

2.4756%

0.0208

64.6895%

0.8964%

GPU72

2⁶²

0.3092

66.1290%

8000

100000

0.0012

1.1980%

0.3105

66.5348%

0.4058%

Difference

+14.6477

+2.5277%

-8000

-100000

-0.0012

-1.1980%

+14.6465

+2.1219%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1986631	40129946201	11	35.224	10100 2² × 5² × 101	-	25	101	2.733e-9	2.778e-6	4.851e-6
1986631	662265609459085362791	21	69.166	166680578693045 5 × 113 × 6679 × 44169767	2021-04-27	6679	44169767	69.540	0.2300	0.4285

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1986631

40129946201

35.224

10100
2² × 5² × 101

101

2.733e-9

2.778e-6

4.851e-6

1986631

662265609459085362791

69.166

166680578693045
5 × 113 × 6679 × 44169767

2021-04-27

6679

44169767

69.540

0.2300

0.4285

exponent	prime factors	composite factor	digits	bits*
1986631	40129946201 662265609459085362791	26576683278365572319469397206991	32	104.390

exponent

prime factors

composite factor

digits

bits*

1986631

40129946201
662265609459085362791

26576683278365572319469397206991

104.390

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.585 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	3.585 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.306	27.104%
25	50000	0.121	88.635%
30	250000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.690
50000	6750000		7	0.675
50000	6750000	662265609459085362791	2	0.193
50000	7034571		7	0.689
100000	10000000		2	0.338

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-23T18:49:33	Oliver Kruse	O2.261	50000	5000000						3	0.254
2019-04-20T12:40:37	MarkS	laptop64	50000	5000000						3	0.254
2021-01-27T21:27:20	Peredron	Peredron2	100000	10000000						1	0.169
2021-01-28T14:10:28	Peredron	Peredron2	100000	10000000						1	0.169
2021-04-27T01:13:23	nordi	sweet16	50000	6750000	662265609459085362791	69.166	2	2	5607759689287547	2	0.193
2021-05-30T08:01:39	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.592
2021-08-31T06:08:29	Dylan Delgado	laptop-ryzen73700	50000	6750000						7	0.675
2021-12-26T12:47:23	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.592
2022-05-12T12:19:15	debrouxl	dl380g9-1	50000	7034571						7	0.689

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T14:40:19

Oliver Kruse

GTX-2

40129946201

28EB2233FF8EBC__

2017-11-12T17:19:27

kkmrkkblmbrbk

c4.xlarge

40129946201

28EB2233FF8EBC__

2021-04-27T14:14:52

mrh

40129946201

662265609459085362791

6D7B64817FB638DE

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

10⁰

10¹

10²

10³

10⁴

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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