M2100941 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	14.1431	67.1642%	500000	15000000	0.1230	5.1535%	14.2661	68.8564%	1.6922%
PrimeNet	2⁵⁸	0.0183	62.0690%	9000	160000	0.0016	2.6780%	0.0199	63.0848%	1.0158%
GPU72	2⁶²	0.2924	64.5161%	10000	140000	0.0016	1.4514%	0.2941	65.0312%	0.5150%
Difference	+5	+13.8507	+2.6481%	+490000	+14860000	+0.1214	+3.7020%	+13.9721	+3.8252%	+3.8252%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.1431

67.1642%

500000

15000000

0.1230

5.1535%

14.2661

68.8564%

1.6922%

PrimeNet

2⁵⁸

0.0183

62.0690%

9000

160000

0.0016

2.6780%

0.0199

63.0848%

1.0158%

GPU72

2⁶²

0.2924

64.5161%

10000

140000

0.0016

1.4514%

0.2941

65.0312%

0.5150%

Difference

+13.8507

+2.6481%

+490000

+14860000

+0.1214

+3.7020%

+13.9721

+3.8252%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2100941	12605647	8	23.588	3 3	-	1	3	5.323e-13	1.057e-7	1.940e-7
2100941	271454182847	12	37.982	64603 7 × 11 × 839	2008-07-14	11	839	1.728e-8	5.350e-6	8.144e-6
2100941	240468035980266137663	21	67.704	57228650395291 17 × 401 × 8394990523	2019-08-30	401	8394990523	17.195	43.606	81.443

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2100941

12605647

23.588

3
3

5.323e-13

1.057e-7

1.940e-7

2100941

271454182847

37.982

64603
7 × 11 × 839

2008-07-14

839

1.728e-8

5.350e-6

8.144e-6

2100941

240468035980266137663

67.704

57228650395291
17 × 401 × 8394990523

2019-08-30

401

8394990523

17.195

43.606

81.443

exponent	prime factors	composite factor	digits	bits*
2100941	12605647 271454182847	3421855605642737009	19	61.569
2100941	12605647 240468035980266137663	3031255176350533897433182961	28	91.292
2100941	271454182847 240468035980266137663	65276054207846139016894475266561	32	105.686
2100941	12605647 271454182847 240468035980266137663	822846896896973058759898791460498869967	39	129.274

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:12:54	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 12605647 skipped known factor: 271454182847	-	-	0.123	-	-	5.153%

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.702 GHz-days
Estimated T-Level:	0.950

Digits	B1	Curves	Complete	FacMiss
20	11000	19 / 100	0.190	82.617%
25	50000	19 / 280	0.068	93.428%

New Calculation Method

Total ECM effort:	1.702 GHz-days
Estimated T-Level:	0.950

Digits	B1	Complete	FacMiss
20	11000	0.628	53.340%
25	50000	0.057	94.446%
30	250000	0.004	99.648%

ECM Summary

B1	B2	factor	curves	GHz-days
		271454182847	1	0.00000e+0
50000	5000000		10	0.851
50000	5000000	240468035980266137663	2	0.170
50000	6750000		7	0.681

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-14T20:20:00	George Woltman	Manual testing			271454182847	37.982		1		1	-
2018-01-05T08:04:54	ATH	ec2-1xd	50000	5000000						3	0.255
2019-08-30T18:59:37	MarkS	laptop64	50000	5000000	240468035980266137663	67.704	2	2		2	0.170
2021-09-28T01:15:57	Dylan Delgado	colab	50000	6750000						7	0.681
2022-02-17T21:51:24	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.596

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T00:24:40

Oliver Kruse

GTX-1

12605647

271454182847

09006D1283F81C__

2017-11-17T03:47:33

kkmrkkblmbrbk

c4.xlarge

12605647

271454182847

09006D1283F81C__

2019-08-31T04:53:33

mnd9

75211b

12605647

271454182847

240468035980266137663

5DAEB3FB032DC4B9

2019-09-01T04:34:31

kkmrkkblmbrbk

c5.large

12605647

271454182847

240468035980266137663

5DAEB3FB032DC4B9

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 = 15000000 (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

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