M1723027 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	17.2452	68.6567%	3642200	123456789	0.6940	8.6227%	17.9392	71.3594%	2.7026%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0010	2.7942%	0.0122	64.1874%	1.0295%
GPU72	2⁶¹	0.1783	65.5738%	7000	110000	0.0009	1.3442%	0.1791	66.0365%	0.4627%
Difference	+6	+17.0669	+3.0829%	+3635200	+123346789	+0.6931	+7.2785%	+17.7601	+5.3228%	+5.3228%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1723027	42563869427280596889881	23	75.172	12351480686977220 2² × 5 × 79 × 151 × 51770813509	2020-04-13	151	51770813509	8,382.2	192.48	359.50
1723027	2727262720466342841204407	25	81.174	791416130004446489 59 × 11524993 × 1163890747	2016-11-20	11524993	1163890747	308,160	5.0709	8.0821

exponent	prime factors	composite factor	digits	bits*
1723027	42563869427280596889881 2727262720466342841204407	116082854327819478678491825852145014660390905567	48	156.346

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	90000	1507500		-		-	-	0.011	-	-	2.357%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.885%
2014-05-04T12:46:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.010	-	-	1.111%
2014-10-07T22:12:00	Jocelyn Larouche	Manual testing	187251	187251		-		-	-	0.013	-	-	1.248%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	280876	280876		-		-	-	0.019	-	-	1.525%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	373844	373844		-		-	-	0.026	-	-	1.741%
2015-02-22T09:50:00	Jocelyn Larouche	Manual testing	411228	411228		-		-	-	0.028	-	-	1.816%
2015-03-06T12:09:00	Jocelyn Larouche	Manual testing	452350	452350		-		-	-	0.031	-	-	1.894%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	497585	497585		-		-	-	0.034	-	-	1.973%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	602077	602077		-		-	-	0.041	-	-	2.137%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	728512	728512		-		-	-	0.050	-	-	2.309%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	801363	801363		-		-	-	0.055	-	-	2.397%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	881499	881499		-		-	-	0.060	-	-	2.487%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	969648	969648		-		-	-	0.066	-	-	2.580%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1066612	1066612		-		-	-	0.073	-	-	2.674%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1173273	1173273		-		-	-	0.080	-	-	2.770%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1290600	1290600		-		-	-	0.088	-	-	2.867%
2015-07-21T01:19:00	Jocelyn Larouche	Manual testing	1419660	1419660		-		-	-	0.097	-	-	2.967%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1561626	1561626		-		-	-	0.107	-	-	3.068%
2015-08-25T02:14:00	mikr	MSI	3642200	123456789		-		-	-	0.694	-	-	8.623%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁵⁷	2⁶⁰		-	-	0.078	-	-
2010-04-24T12:42:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.089	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.178	-	-
2010-10-27T20:37:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.926	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.570	-	-
2015-05-03T20:03:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.139	-	-
2015-05-03T20:03:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.168	-	-
2015-09-02T13:37:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.337	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.941 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:	14.941 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		172	10.24
50000	5000000	42563869427280596889881	78	4.643
50000	5000000	2727262720466342841204407	1	0.060

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-06T14:59:00	paulie	iMac3.4	50000	5000000						3	0.179
2009-09-26T15:45:00	ekrumme	nuanceH2	50000	5000000						3	0.179
2010-07-25T08:08:00	unconnected	X3220--xp	50000	5000000						3	0.179
2011-12-07T11:19:00	Bud	annan	50000	5000000						3	0.179
2013-04-28T17:18:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-01-24T19:34:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-10-31T04:08:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2015-07-02T02:05:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2015-10-26T13:06:30	mikr	MSI	50000	5000000						12	0.714
2016-09-19T18:22:50	Bruce	DESK3	50000	5000000						3	0.179
2016-11-20T22:55:52	Bruce	DESK3	50000	5000000	2727262720466342841204407	81.174	1	2		1	0.060
2020-04-13T10:22:22	TJAOI	Manual testing	50000	5000000	42563869427280596889881	75.172	78	2		78	4.643
2020-04-13T10:22:22	TJAOI	Manual testing	50000	5000000						133	7.917

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	695E872CA3CD0901	0.081
2015-07-03T04:32:00	MadPoo	Manual testing	695E872CA3CD0901	0.081

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T04:21:33

Oliver Kruse

GTX-3

2727262720466342841204407

56CC8742C1B7B1__

2017-11-03T15:44:08

kkmrkkblmbrbk

c4.xlarge

2727262720466342841204407

56CC8742C1B7B1__

2020-04-13T19:23:33

CrypticClue

cruncher

42563869427280596889881

2727262720466342841204407

DE0E0CAD925516CD

2020-04-13T22:29:24

Igvan28

MineOld

42563869427280596889881

2727262720466342841204407

DE0E0CAD925516CD

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 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 1561626 (P-1 stage 1)

B1 = 1419660 (P-1 stage 1)

B1 = 1290600 (P-1 stage 1)

B1 = 1173273 (P-1 stage 1)

B1 = 1066612 (P-1 stage 1)

B1 = 969648 (P-1 stage 1)

B1 = 881499 (P-1 stage 1)

B1 = 801363 (P-1 stage 1)

B1 = 728512 (P-1 stage 1)

B1 = 602077 (P-1 stage 1)

B1 = 497585 (P-1 stage 1)

B1 = 452350 (P-1 stage 1)

B1 = 411228 (P-1 stage 1)

B1 = 373844 (P-1 stage 1)

B1 = 280876 (P-1 stage 1)

B1 = 187251 (P-1 stage 1)

B1 = 90000, B2 = 1507500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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