M1971601 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	15.0710	68.6567%	-	-	-	-	15.0710	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0014	2.4720%	0.0209	64.6881%	0.8950%
GPU72	2⁶²	0.3116	66.1290%	8000	100000	0.0012	1.1961%	0.3128	66.5342%	0.4051%
Difference	+5	+14.7594	+2.5277%	-8000	-100000	-0.0012	-1.1961%	+14.7581	+2.1226%	+2.1226%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.0710

68.6567%

15.0710

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0014

2.4720%

0.0209

64.6881%

0.8950%

GPU72

2⁶²

0.3116

66.1290%

8000

100000

0.0012

1.1961%

0.3128

66.5342%

0.4051%

Difference

+14.7594

+2.5277%

-8000

-100000

-0.0012

-1.1961%

+14.7581

+2.1226%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1971601	2318602777	10	31.111	588 2² × 3 × 7²	-	49	49	1.636e-10	4.672e-6	9.507e-6
1971601	104338236827607942908857	24	76.466	26460281980889628 2² × 3 × 2205023498407469	2021-11-21	4	2205023498407469	10,262	11,453,443	21,391,843

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1971601

2318602777

31.111

588
2² × 3 × 7²

1.636e-10

4.672e-6

9.507e-6

1971601

104338236827607942908857

76.466

26460281980889628
2² × 3 × 2205023498407469

2021-11-21

2205023498407469

10,262

11,453,443

21,391,843

exponent	prime factors	composite factor	digits	bits*
1971601	2318602777 104338236827607942908857	241918925655775446695733298095889	33	107.576

exponent

prime factors

composite factor

digits

bits*

1971601

2318602777
104338236827607942908857

241918925655775446695733298095889

107.576

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.438 GHz-days
Estimated T-Level:	1.950

Digits	B1	Curves	Complete	FacMiss
20	11000	39 / 100	0.390	67.573%
25	50000	39 / 280	0.139	86.976%

New Calculation Method

Total ECM effort:	3.438 GHz-days
Estimated T-Level:	1.950

Digits	B1	Complete	FacMiss
20	11000	1.281	27.771%
25	50000	0.116	89.086%
30	250000	0.007	99.290%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.689
50000	5000000	104338236827607942908857	5	0.422
50000	6293304		7	0.653
50000	6750000		7	0.674

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-21T12:38:39	ATH	ec2-1xe	50000	5000000						3	0.253
2019-03-30T05:30:52	-Anonymous-		50000	5000000						3	0.253
2021-01-27T06:50:26	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.591
2021-05-11T00:43:03	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.591
2021-08-15T03:00:23	happy5214	Focus	50000	6750000						7	0.674
2021-11-21T01:11:54	MarkS	desktop-i7	50000	5000000	104338236827607942908857	76.466	5	2	5460216311100591	5	0.422
2022-05-10T11:34:21	debrouxl	z400	50000	6293304						7	0.653

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T10:44:39

Oliver Kruse

GTX-1

2318602777

7408ED904FAA96__

2017-11-12T04:30:51

kkmrkkblmbrbk

c4.xlarge

2318602777

7408ED904FAA96__

2021-11-21T08:18:14

MarkS

desktop-i7

2318602777

104338236827607942908857

3313337F17C093D0

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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