M1782839 Mersenne number exponent details

Residue

Status

L-L

7522D5135075E542

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	16.6666	68.6567%	500000	15000000	0.1015	5.0527%	16.7681	70.2404%	1.5837%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8124%	0.0120	64.1940%	1.0361%
GPU72	2⁶¹	0.1723	65.5738%	8000	130000	0.0012	1.4921%	0.1735	66.0875%	0.5137%
Difference	+6	+16.4943	+3.0829%	+492000	+14870000	+0.1003	+3.5605%	+16.5947	+4.1529%	+4.1529%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6666

68.6567%

500000

15000000

0.1015

5.0527%

16.7681

70.2404%

1.5837%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8124%

0.0120

64.1940%

1.0361%

GPU72

2⁶¹

0.1723

65.5738%

8000

130000

0.0012

1.4921%

0.1735

66.0875%

0.5137%

Difference

+16.4943

+3.0829%

+492000

+14870000

+0.1003

+3.5605%

+16.5947

+4.1529%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1782839	385354906656477957623	21	68.385	108073389312349 3940253 × 27428033	2015-02-12	3940253	27428033	39.014	0.4106	0.6308

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1782839

385354906656477957623

68.385

108073389312349
3940253 × 27428033

2015-02-12

3940253

27428033

39.014

0.4106

0.6308

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:50:00	Carsten Kossendey	leela	95000	1615000		-		-	-	0.014	-	-	2.435%
2014-04-10T20:52:00	ANONYMOUS	Manual testing	100000	100000		-		-	-	0.008	-	-	0.891%
2014-05-09T20:32:00	Jocelyn Larouche	Manual testing	136001	136001		-		-	-	0.011	-	-	1.060%
2014-09-19T20:39:00	Jocelyn Larouche	Manual testing	172002	172002		-		-	-	0.014	-	-	1.201%
2016-03-16T12:33:30	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.053%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2010-04-20T22:46:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.086	-	-
2010-10-16T22:16:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.895	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.768 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:	17.768 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	17.70
50000	5000000	385354906656477957623	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-23T15:39:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-07T03:44:00	SubPrime	stor	50000	5000000						3	0.207
2010-12-22T03:50:00	Lupo	yorick	50000	5000000						3	0.207
2012-02-17T23:33:00	S36049	Wolle5	50000	5000000						3	0.207
2013-06-17T05:39:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-02-18T06:53:00	Bruce	snowflake	50000	5000000						3	0.207
2015-02-12T19:25:00	Chang Chia-Tche	exbpc13	50000	5000000	385354906656477957623	68.385	1	2		1	0.069
2020-06-29T14:19:39	nordi	sweet16	50000	5000000						3	0.207
2020-07-26T15:02:08	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.207
2020-10-05T16:15:24	nordi	sweet16	50000	5000000						7	0.482
2020-11-13T10:46:23	TJAOI	Manual testing	50000	5000000						226	15.56

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	7522D5135075E542	0.097

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

ANONYMOUS

v4_computers

7522D5135075E542

0.097

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)

B1 = 95000, B2 = 1615000 (P-1 stage 2)

B1 = 172002 (P-1 stage 1)

B1 = 136001 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

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