M1951837 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	15.2236	68.6567%	500000	15000000	0.1015	5.1081%	15.3250	70.2578%	1.6010%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4672%	0.0209	64.6864%	0.8933%
GPU72	2⁶²	0.3148	66.1290%	8000	90000	0.0010	1.1533%	0.3157	66.5197%	0.3906%
Difference	+5	+14.9088	+2.5277%	+492000	+14910000	+0.1005	+3.9547%	+15.0093	+3.7381%	+3.7381%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2236

68.6567%

500000

15000000

0.1015

5.1081%

15.3250

70.2578%

1.6010%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4672%

0.0209

64.6864%

0.8933%

GPU72

2⁶²

0.3148

66.1290%

8000

90000

0.0010

1.1533%

0.3157

66.5197%

0.3906%

Difference

+14.9088

+2.5277%

+492000

+14910000

+0.1005

+3.9547%

+15.0093

+3.7381%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1951837	58555111	8	25.803	15 3 × 5	-	3	5	2.298e-12	2.446e-7	4.803e-7
1951837	2432203604071	13	41.145	623055 3 × 5 × 73 × 569	2008-07-15	73	569	2.792e-7	7.868e-6	1.169e-5
1951837	7728724767667334569	19	62.745	1979859170532 2² × 3 × 43 × 6043 × 634939	2015-10-03	6043	634939	0.3161	0.0032	0.0051
1951837	478698425277024085040689	24	78.663	122627664419985912 2³ × 3 × 11 × 1283 × 362041098101	2020-11-24	1283	362041098101	45,701	1,551.6	2,898.0

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1951837

58555111

25.803

15
3 × 5

2.298e-12

2.446e-7

4.803e-7

1951837

2432203604071

41.145

623055
3 × 5 × 73 × 569

2008-07-15

569

2.792e-7

7.868e-6

1.169e-5

1951837

7728724767667334569

62.745

1979859170532
2² × 3 × 43 × 6043 × 634939

2015-10-03

6043

634939

0.3161

0.0032

0.0051

1951837

478698425277024085040689

78.663

122627664419985912
2³ × 3 × 11 × 1283 × 362041098101

2020-11-24

1283

362041098101

45,701

1,551.6

2,898.0

exponent	prime factors	composite factor	digits	bits*
1951837	58555111 2432203604071	142417952010977456881	21	66.949
1951837	58555111 7728724767667334569	452556336659209986761932159	27	88.548
1951837	2432203604071 7728724767667334569	18797832234793293270299967430399	32	103.890
1951837	58555111 478698425277024085040689	28030239427621351049230983911479	32	104.467
1951837	2432203604071 478698425277024085040689	1164292035221890266225434982481044919	37	119.809
1951837	58555111 2432203604071 7728724767667334569	1100709153067699349497967596183398219289	40	129.694
1951837	7728724767667334569 478698425277024085040689	3699728375681886889422708850437710541278041	43	141.408
1951837	58555111 2432203604071 478698425277024085040689	68175249358833694168649896422460640628031009	44	145.612
1951837	58555111 7728724767667334569 478698425277024085040689	21663800570790258749959144265806253933040577261755 1	51	167.212
1951837	2432203604071 7728724767667334569 478698425277024085040689	89984926894172319646476759146263088843863195346905 04911	55	182.554
1951837	58555111 2432203604071 7728724767667334569 478698425277024085040689	52690773826151454300269273907297004024552710723527 0865709650121	63	208.357

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-10-03T22:21:33	alpertron	Manual testing	500000	15000000	12		7728724767667334569	19	62.745	0.101	0.212	0.203	5.108%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-10-03T22:21:33

alpertron

Manual testing

500000

15000000

7728724767667334569

62.745

0.101

0.212

0.203

5.108%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	2432203604071	41.145	13	1.29135e-7	0.235	2.86338e-7

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:48:00

J Feitsma

Manual testing

2432203604071

41.145

1.29135e-7

0.235

2.86338e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.988 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	20.988 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.078	0.011%
25	50000	0.806	44.655%
30	250000	0.050	95.125%
35	1000000	0.002	99.770%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4610683		14	0.944
50000	5000000		18	1.253
50000	5000000	478698425277024085040689	5	0.348
50000	6750000		7	0.556
50000	7500000		214	17.89

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-07-22T03:25:07	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-13T13:35:17	ATH	ec2-ECMCF	50000	5000000						3	0.209
2020-11-24T12:43:42	nordi	sweet16	50000	5000000	478698425277024085040689	78.663	5	2	8732859073892162	5	0.348
2021-01-27T18:28:45	seatsea	dt	50000	4610683						7	0.472
2021-05-07T05:52:15	Team_Inspector	SpudBoy4	50000	6750000						7	0.556
2021-07-14T09:03:40	seatsea	Manual testing	50000	4610683						7	0.472
2021-11-14T11:50:19	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-04-02T19:33:51	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.487
2022-05-12T09:17:36	TJAOI	Manual testing	50000	7500000						214	17.89

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:28:59

alpertron

Manual testing

58555111

2432203604071

7728724767667334569

130C3867B1B189__

2017-10-20T12:23:16

Oliver Kruse

GTX-0

58555111

2432203604071

7728724767667334569

130C3867B1B189__

2020-11-25T11:03:43

rbanov

ccg_lnx01

58555111

2432203604071

7728724767667334569

478698425277024085040689

5D3B04A44271756D

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

10¹¹

10¹²

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