M1918537 Mersenne number exponent details

Residue

Status

L-L

932BF001146560EB

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	15.4878	68.6567%	500000	15000000	0.1015	5.0975%	15.5893	70.2544%	1.5977%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0924%	0.0114	64.2972%	1.1393%
GPU72	2⁶¹	0.1601	65.5738%	10000	170000	0.0015	1.7613%	0.1616	66.1801%	0.6063%
Difference	+6	+15.3277	+3.0829%	+490000	+14830000	+0.1000	+3.3362%	+15.4277	+4.0743%	+4.0743%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.4878

68.6567%

500000

15000000

0.1015

5.0975%

15.5893

70.2544%

1.5977%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0924%

0.0114

64.2972%

1.1393%

GPU72

2⁶¹

0.1601

65.5738%

10000

170000

0.0015

1.7613%

0.1616

66.1801%

0.6063%

Difference

+15.3277

+3.0829%

+490000

+14830000

+0.1000

+3.3362%

+15.4277

+4.0743%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1918537	1399166912079670326361	22	70.245	364644234664140 2² × 3 × 5 × 247717 × 24533657	2009-08-02	247717	24533657	171.49	0.1236	0.1964

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1918537

1399166912079670326361

70.245

364644234664140
2² × 3 × 5 × 247717 × 24533657

2009-08-02

247717

24533657

171.49

0.1236

0.1964

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:18:58	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.097%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:18:58

alpertron

Manual testing

500000

15000000

0.101

-

-

5.097%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-12-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2022-03-09T05:13:25	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.080	-	-
2009-06-02T03:29:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.080	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.779 GHz-days
Estimated T-Level:	24.554

Digits	B1	Curves	Complete	FacMiss
20	11000	255 / 100	2.550	7.709%
25	50000	255 / 280	0.911	40.158%

New Calculation Method

Total ECM effort:	19.779 GHz-days
Estimated T-Level:	24.554

Digits	B1	Complete	FacMiss
20	11000	10.548	0.003%
25	50000	0.971	37.883%
30	250000	0.062	94.023%
35	1000000	0.003	99.711%

ECM Summary

B1	B2	factor	curves	GHz-days
		1399166912079670326361	1	0.00000e+0
50000	5000000		24	1.667
50000	6600000		217	17.00
50000	6750000		14	1.109

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-09T04:06:00	paulie	iMac3.4	50000	5000000						3	0.208
2009-08-02T11:58:00	SubPrime	abd0			1399166912079670326361	70.245		1		1	-
2020-10-23T21:08:36	nordi	sweet16	50000	5000000						7	0.486
2021-01-15T18:47:52	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-04-12T19:28:07	MarkS	desktop-i7	50000	5000000						7	0.486
2021-07-22T01:23:35	happy5214	Focus	50000	6750000						7	0.554
2021-10-16T01:07:42	Dylan Delgado	colab	50000	6750000						7	0.554
2022-02-03T11:48:00	TJAOI	Manual testing	50000	6600000						217	17.00

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	932BF001146560EB	0.104

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

932BF001146560EB

0.104

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)

10⁴

10⁵

10⁶

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