M1935677 Mersenne number exponent details

Residue

Status

L-L

3D7B00206C51F66B

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	15.3507	68.6567%	1000000	30000000	0.2029	6.2307%	15.5536	70.6096%	1.9529%
PrimeNet	2⁵⁸	0.0198	63.7931%	8000	140000	0.0012	2.4632%	0.0210	64.6850%	0.8919%
GPU72	2⁶²	0.3174	66.1290%	8000	90000	0.0010	1.1513%	0.3184	66.5190%	0.3900%
Difference	+5	+15.0333	+2.5277%	+992000	+29910000	+0.2020	+5.0795%	+15.2352	+4.0906%	+4.0906%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.3507

68.6567%

1000000

30000000

0.2029

6.2307%

15.5536

70.6096%

1.9529%

PrimeNet

2⁵⁸

0.0198

63.7931%

8000

140000

0.0012

2.4632%

0.0210

64.6850%

0.8919%

GPU72

2⁶²

0.3174

66.1290%

8000

90000

0.0010

1.1513%

0.3184

66.5190%

0.3900%

Difference

+15.0333

+2.5277%

+992000

+29910000

+0.2020

+5.0795%

+15.2352

+4.0906%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1935677	5186234941880881566407	22	72.135	1339643685873439 495797 × 2702000387	2017-02-27	495797	2702000387	727.12	11.617	21.628

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1935677

5186234941880881566407

72.135

1339643685873439
495797 × 2702000387

2017-02-27

495797

2702000387

727.12

11.617

21.628

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-11-20T04:38:00	kurly	Manual testing	1000000	30000000		-		-	-	0.203	-	-	6.231%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-11-20T04:38:00

kurly

Manual testing

1000000

30000000

0.203

-

-

6.231%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.060	-	-
2010-02-02T07:27:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.079	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.159	-	-
2011-08-27T22:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.825	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.507	-	-
2015-05-13T22:18:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	1.014	-	-
2015-05-13T22:18:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.930	-	-
2015-09-04T17:59:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.861	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.325 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:	19.325 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.547	0.019%
25	50000	0.775	46.088%
30	250000	0.048	95.321%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.085
50000	5000000	5186234941880881566407	3	0.209
50000	6600000		210	16.48
50000	6750000		7	0.555

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-12T19:41:00	paulie	iMac3.4	50000	5000000						3	0.209
2009-08-07T16:15:00	SubPrime	pitr	50000	5000000						3	0.209
2010-12-30T01:19:00	James Hintz	ryan	50000	5000000						3	0.209
2012-11-18T18:28:00	Donna Noble	PH2x6	50000	5000000						3	0.209
2013-12-17T10:46:00	OS1	L3	50000	5000000						3	0.209
2015-03-30T20:13:00	arnaud	CHAMOT22	50000	5000000						3	0.209
2015-10-10T07:06:17	Chris Smith	starcraft2	50000	5000000						3	0.209
2016-03-12T22:39:18	Bruce	Desk6	50000	5000000						3	0.209
2016-06-21T18:26:06	Jason U	Server7	50000	5000000						3	0.209
2016-09-21T03:05:07	Bruce	Desk6	50000	5000000						3	0.209
2017-02-27T21:58:08	Bruce	Desk6	50000	5000000	5186234941880881566407	72.135	3	2		3	0.209
2021-11-18T09:18:28	LordJulius	surface7	50000	6750000						7	0.555
2022-03-10T10:41:20	TJAOI	Manual testing	50000	6600000						210	16.48

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	3D7B00206C51F66B	0.105
2015-06-27T00:56:00	MadPoo	Manual testing	3D7B00206C51F66B	0.105

date

userid

compid

res64

spent (GHz-days)

1999-01-10T00:00:00

ANONYMOUS

v4_computers

3D7B00206C51F66B

0.105

2015-06-27T00:56:00

MadPoo

Manual testing

3D7B00206C51F66B

0.105

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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