M1909703 Mersenne number exponent details

Residue

Status

L-L

F55D22EDA9D27AA7

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	2⁶⁸	31.2116	69.1176%	8000000	320000000	1.9665	9.7351%	33.1780	72.1241%	3.0064%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0409%	0.0114	64.2782%	1.1203%
GPU72	2⁶¹	0.1609	65.5738%	10000	170000	0.0015	1.7597%	0.1623	66.1796%	0.6058%
Difference	+7	+31.0507	+3.5439%	+7990000	+319830000	+1.9650	+7.9754%	+33.0157	+5.9445%	+5.9445%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

31.2116

69.1176%

8000000

320000000

1.9665

9.7351%

33.1780

72.1241%

3.0064%

PrimeNet

2⁵⁷

0.0101

63.1579%

9000

160000

0.0014

3.0409%

0.0114

64.2782%

1.1203%

GPU72

2⁶¹

0.1609

65.5738%

10000

170000

0.0015

1.7597%

0.1623

66.1796%

0.6058%

Difference

+31.0507

+3.5439%

+7990000

+319830000

+1.9650

+7.9754%

+33.0157

+5.9445%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1909703	312645424055403781490041	24	78.049	81857080408682340 2² × 3² × 5 × 822791 × 552706043	2020-04-08	822791	552706043	34,137	2.4300	4.4242

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1909703

312645424055403781490041

78.049

81857080408682340
2² × 3² × 5 × 822791 × 552706043

2020-04-08

822791

552706043

34,137

2.4300

4.4242

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-06-14T18:15:00	kurly	kurlytop	1000000	30000000		-		-	-	0.203	-	-	5.682%
2017-12-06T16:28:50	mikr	S063	8000000	320000000	12	-		-	-	1.966	-	-	9.735%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-06-14T18:15:00

kurly

kurlytop

1000000

30000000

0.203

-

-

5.682%

2017-12-06T16:28:50

mikr

S063

8000000

320000000

1.966

-

-

9.735%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2¹	2⁵⁶		-	-	0.005	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁶	2⁵⁷		-	-	0.005	-	-
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁷	2⁵⁸		-	-	0.010	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁸	2⁵⁹		-	-	0.020	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁹	2⁶⁰		-	-	0.040	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁶⁰	2⁶¹		-	-	0.080	-	-
2009-05-27T10:09:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.080	-	-
2011-03-07T00:25:00	GrunwalderGIMP	GWPrime02	2⁶¹	2⁶²		-	-	0.161	-	-
2011-03-07T03:53:00	GrunwalderGIMP	GWPrime02	2⁶²	2⁶³		-	-	0.514	-	-
2015-05-18T08:20:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.028	-	-
2015-05-19T20:04:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	1.957	-	-
2015-09-01T08:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.913	-	-
2017-03-15T08:26:28	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.826	-	-
2019-04-27T00:32:11	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.65	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.703 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	18.703 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.417	0.022%
25	50000	0.762	46.675%
30	250000	0.047	95.402%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		105	7.288
50000	5000000	312645424055403781490041	2	0.139
50000	6600000		144	11.28

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-28T21:11:00	Lupo	yorick	50000	5000000						3	0.208
2009-08-01T00:55:00	James Hintz	19_071509	50000	5000000						3	0.208
2010-11-30T04:46:00	Lupo	yorick	50000	5000000						3	0.208
2012-10-21T00:29:00	Bud	annan	50000	5000000						3	0.208
2013-11-23T01:59:00	Bruce	apandya-DESK11	50000	5000000						3	0.208
2014-10-08T08:41:00	Sara	Sara	50000	5000000						3	0.208
2015-08-05T16:57:00	Sara	Sara	50000	5000000						3	0.208
2016-01-28T22:53:44	Sara	Sara	50000	5000000						3	0.208
2016-06-15T17:58:29	Bruce	test	50000	5000000						3	0.208
2016-08-21T13:09:18	Bruce	test	50000	5000000						3	0.208
2017-02-04T19:54:37	Bruce	Desk6	50000	5000000						3	0.208
2017-07-24T13:40:26	Bruce	Desk6	50000	5000000						3	0.208
2017-12-08T00:01:03	Yan Jinzhao	cndns	50000	5000000						3	0.208
2018-04-08T07:12:16	Bruce	Desk6	50000	5000000						3	0.208
2018-09-14T12:19:04	Bruce	Desk6	50000	5000000						3	0.208
2019-12-01T11:45:16	nokno	leo231	50000	5000000						3	0.208
2019-12-01T15:06:51	LordJulius	BlackboxNouveau	50000	5000000						3	0.208
2019-12-05T20:58:16	mnd9	50871b	50000	5000000						3	0.208
2019-12-09T19:24:34	daveward2005	Davy	50000	5000000						3	0.208
2019-12-18T21:34:05	nranks	wlaptop	50000	5000000						3	0.208
2019-12-19T08:36:25	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2019-12-26T07:23:36	mnd9	50871b	50000	5000000						3	0.208
2019-12-31T00:27:42	J.R. Allen	lapacer	50000	5000000						3	0.208
2020-01-04T17:45:53	TheJudger	myECM	50000	5000000						3	0.208
2020-01-13T13:55:23	mnd9	colab2	50000	5000000						3	0.208
2020-01-19T22:08:10	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.208
2020-01-26T05:31:13	mnd9	25836b	50000	5000000						3	0.208
2020-02-02T23:38:44	David_McCann	i5	50000	5000000						3	0.208
2020-02-11T21:40:52	David_McCann	i5	50000	5000000						3	0.208
2020-02-18T07:38:47	IanGlencross	glenx24	50000	5000000						3	0.208
2020-02-25T13:40:03	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.208
2020-03-03T15:54:00	mnd9	kitchen	50000	5000000						3	0.208
2020-03-09T17:20:41	Keysarecool	HPLaptop	50000	5000000						3	0.208
2020-03-17T08:49:58	mnd9	office2	50000	5000000						3	0.208
2020-03-27T13:47:06	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2020-04-08T14:21:33	Keysarecool	HPLaptop	50000	5000000	312645424055403781490041	78.049	2	2	3457673439644061	2	0.139
2021-12-23T11:05:23	TJAOI	Manual testing	50000	6600000						144	11.28

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	F55D22EDA9D27AA7	0.104
2015-07-14T15:04:00	MadPoo	Manual testing	F55D22EDA9D27AA7	0.104

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

ANONYMOUS

v4_computers

F55D22EDA9D27AA7

0.104

2015-07-14T15:04:00

MadPoo

Manual testing

F55D22EDA9D27AA7

0.104

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