M1872097 Mersenne number exponent details

Residue

Status

L-L

EB6D1DEBAAE0E11C

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	15.8720	68.6567%	500000	15000000	0.1015	5.0825%	15.9735	70.2497%	1.5930%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0297%	0.0116	64.2741%	1.1162%
GPU72	2⁶¹	0.1641	65.5738%	10000	150000	0.0014	1.6900%	0.1655	66.1556%	0.5818%
Difference	+6	+15.7079	+3.0829%	+490000	+14850000	+0.1001	+3.3925%	+15.8080	+4.0942%	+4.0942%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.8720

68.6567%

500000

15000000

0.1015

5.0825%

15.9735

70.2497%

1.5930%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0297%

0.0116

64.2741%

1.1162%

GPU72

2⁶¹

0.1641

65.5738%

10000

150000

0.0014

1.6900%

0.1655

66.1556%

0.5818%

Difference

+15.7079

+3.0829%

+490000

+14850000

+0.1001

+3.3925%

+15.8080

+4.0942%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1872097	852200916293677933537	21	69.530	227605972418544 2⁴ × 3 × 29 × 163510037657	2009-07-22	29	163510037657	86.498	700.76	1,308.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1872097

852200916293677933537

69.530

227605972418544
2⁴ × 3 × 29 × 163510037657

2009-07-22

163510037657

86.498

700.76

1,308.8

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:38:16	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.082%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:38:16

alpertron

Manual testing

500000

15000000

0.101

-

-

5.082%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-01-09T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.021

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.189 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	19.189 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	10.295	0.003%
25	50000	0.947	38.771%
30	250000	0.060	94.165%
35	1000000	0.003	99.718%

ECM Summary

B1	B2	factor	curves	GHz-days
		852200916293677933537	1	0.00000e+0
50000	5000000		38	2.631
50000	6600000		212	16.56

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-29T06:25:00	paulie	iMac3.4	50000	5000000						3	0.208
2009-07-22T23:43:00	SubPrime	abd1			852200916293677933537	69.530		1		1	-
2015-03-10T15:46:00	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2020-07-04T08:09:26	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.208
2020-08-05T11:54:27	Ahmed Azhad	c5.xlarge.az	50000	5000000						3	0.208
2020-10-12T00:37:39	nordi	sweet16	50000	5000000						7	0.485
2020-12-14T02:44:15	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-03-18T23:59:48	Poao	justg-ZA	50000	5000000						7	0.485
2021-07-11T20:38:58	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.485
2021-09-10T07:34:27	TJAOI	Manual testing	50000	6600000						212	16.56

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	EB6D1DEBAAE0E11C	0.102

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

ANONYMOUS

v4_computers

EB6D1DEBAAE0E11C

0.102

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