M1795921 Mersenne number exponent details

Residue

Status

L-L

849A5E2E1A9E357B

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	16.5452	68.6567%	500000	15000000	0.1015	5.0571%	16.6467	70.2418%	1.5851%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8162%	0.0119	64.1955%	1.0376%
GPU72	2⁶¹	0.1710	65.5738%	8000	130000	0.0012	1.4944%	0.1722	66.0882%	0.5145%
Difference	+6	+16.3742	+3.0829%	+492000	+14870000	+0.1003	+3.5627%	+16.4745	+4.1535%	+4.1535%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.5452

68.6567%

500000

15000000

0.1015

5.0571%

16.6467

70.2418%

1.5851%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8162%

0.0119

64.1955%

1.0376%

GPU72

2⁶¹

0.1710

65.5738%

8000

130000

0.0012

1.4944%

0.1722

66.0882%

0.5145%

Difference

+16.3742

+3.0829%

+492000

+14870000

+0.1003

+3.5627%

+16.4745

+4.1535%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1795921	4057680052017700135767737	25	81.747	1129693358454436508 2² × 137 × 3989 × 72797 × 7099087	2015-07-01	72797	7099087	475,027	0.0358	0.0568
1795921	3182808254289077482769127038063	31	101.328	886121453641078166235911 11 × 5981 × 36709 × 366905489681669	2015-02-25	36709	366905489681669	9.199e+10	1,572,465	2,936,927

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1795921

4057680052017700135767737

81.747

1129693358454436508
2² × 137 × 3989 × 72797 × 7099087

2015-07-01

72797

7099087

475,027

0.0358

0.0568

1795921

3182808254289077482769127038063

101.328

886121453641078166235911
11 × 5981 × 36709 × 366905489681669

2015-02-25

36709

366905489681669

9.199e+10

1,572,465

2,936,927

exponent	prime factors	composite factor	digits	bits*
1795921	4057680052017700135767737 3182808254289077482769127038063	12914817562826069281538251164995687021070586523326 373431	56	183.075

exponent

prime factors

composite factor

digits

bits*

1795921

4057680052017700135767737
3182808254289077482769127038063

12914817562826069281538251164995687021070586523326
373431

183.075

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:34:00	Carsten Kossendey	leela	95000	1638750		-		-	-	0.014	-	-	2.447%
2014-04-28T23:56:00	ANONYMOUS	Manual testing	145000	145000		-		-	-	0.011	-	-	1.099%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	180739	180739		-		-	-	0.014	-	-	1.234%
2015-01-13T02:42:00	Jocelyn Larouche	Manual testing	271108	271108		-		-	-	0.021	-	-	1.510%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	360842	360842		-		-	-	0.028	-	-	1.724%
2015-02-21T13:42:00	Jocelyn Larouche	Manual testing	396926	396926		-		-	-	0.031	-	-	1.799%
2015-07-01T11:29:00	alpertron	Manual testing	500000	15000000	12		4057680052017700135767737	25	81.747	0.101	0.195	0.203	5.057%

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		-	-	0.021	-	-
2010-04-19T13:16:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.086	-	-
2010-11-18T02:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.889	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.782 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:	17.782 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		255	17.58
50000	5000000	3182808254289077482769127038063	3	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-04T08:18:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-12T02:32:00	SubPrime	mysql0	50000	5000000						3	0.207
2010-11-28T07:56:00	Hunter	Hunter	50000	5000000						3	0.207
2012-03-12T08:32:00	S36049	Wolle5	50000	5000000						3	0.207
2013-07-02T09:08:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-03-16T20:59:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2015-02-25T08:46:00	Chang Chia-Tche	exbpc13	50000	5000000	3182808254289077482769127038063	101.328	3	2		3	0.207
2020-08-15T01:59:39	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-10-17T22:58:48	nordi	sweet16	50000	5000000						7	0.482
2021-01-05T13:39:29	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.482
2021-01-15T10:45:20	TJAOI	Manual testing	50000	5000000						220	15.16

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	849A5E2E1A9E357B	0.097

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

849A5E2E1A9E357B

0.097

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T17:39:15

Oliver Kruse

GTX-1

4057680052017700135767737

3182808254289077482769127038063

56380AF9B75376CA

2017-10-05T21:20:00

Oliver Kruse

Manual testing

4057680052017700135767737

3182808254289077482769127038063

56380AF9B75376__

2017-11-11T03:28:31

kkmrkkblmbrbk

c4.xlarge

4057680052017700135767737

3182808254289077482769127038063

56380AF9B75376__

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 = 396926 (P-1 stage 1)

B1 = 360842 (P-1 stage 1)

B1 = 271108 (P-1 stage 1)

B1 = 180739 (P-1 stage 1)

B1 = 95000, B2 = 1638750 (P-1 stage 2)

B1 = 145000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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