M1735681 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	2⁶⁸	34.3409	69.1176%	2077640	190924910	0.9728	8.1114%	35.3137	71.6227%	2.5050%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7981%	0.0123	64.1888%	1.0309%
GPU72	2⁶¹	0.1770	65.5738%	8000	110000	0.0011	1.4102%	0.1780	66.0593%	0.4855%
Difference	+7	+34.1639	+3.5439%	+2069640	+190814910	+0.9717	+6.7012%	+35.1357	+5.5634%	+5.5634%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1735681	292837502745264012667217	24	77.954	84358100003763368 2³ × 19 × 1146679 × 483995521	2019-11-29	1146679	483995521	27,971	2.1596	3.8742

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:45:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.125%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.768%
2014-05-06T10:52:00	Jocelyn Larouche	Manual testing	136979	136979		-		-	-	0.011	-	-	0.923%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	173958	173958		-		-	-	0.014	-	-	1.053%
2014-12-02T21:55:00	Jocelyn Larouche	Manual testing	210937	210937		-		-	-	0.017	-	-	1.166%
2015-01-27T21:58:00	Jocelyn Larouche	Manual testing	255233	255233		-		-	-	0.020	-	-	1.284%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	280756	280756		-		-	-	0.022	-	-	1.346%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	373685	373685		-		-	-	0.029	-	-	1.543%
2015-02-21T13:42:00	Jocelyn Larouche	Manual testing	411053	411053		-		-	-	0.032	-	-	1.612%
2015-03-08T04:50:00	Jocelyn Larouche	Manual testing	452158	452158		-		-	-	0.036	-	-	1.683%
2015-03-15T18:55:00	Jocelyn Larouche	Manual testing	497373	497373		-		-	-	0.039	-	-	1.755%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	601821	601821		-		-	-	0.047	-	-	1.906%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	728203	728203		-		-	-	0.057	-	-	2.064%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	801023	801023		-		-	-	0.063	-	-	2.146%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	881125	881125		-		-	-	0.069	-	-	2.229%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	969237	969237		-		-	-	0.076	-	-	2.314%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1066160	1066160		-		-	-	0.084	-	-	2.401%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1172776	1172776		-		-	-	0.092	-	-	2.490%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1290053	1290053		-		-	-	0.101	-	-	2.580%
2015-07-21T01:20:00	Jocelyn Larouche	Manual testing	1419058	1419058		-		-	-	0.112	-	-	2.673%
2015-07-27T01:26:00	Jocelyn Larouche	Manual testing	1560963	1560963		-		-	-	0.123	-	-	2.767%
2015-09-17T01:50:00	Jocelyn Larouche	Manual testing	1717059	1717059		-		-	-	0.135	-	-	2.862%
2015-09-27T21:23:22	Jocelyn Larouche	Manual testing	1888764	1888764		-		-	-	0.149	-	-	2.960%
2015-09-28T14:09:53	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	7.968%
2018-10-03T11:47:41	Jocelyn Larouche	low 4M	2077640	17356810	12	-		-	-	0.229	-	-	5.390%
2018-10-11T19:17:51	Jocelyn Larouche	low 4M	2077640	173568100	12	-		-	-	0.898	-	-	8.002%
2018-10-17T22:59:56	Jocelyn Larouche	low 4M	2077640	190924910	12	-		-	-	0.973	-	-	8.111%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.066	-	-
2010-04-22T12:49:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.088	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.177	-	-
2010-11-18T02:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.920	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.566	-	-
2015-05-05T08:43:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.131	-	-
2015-05-05T08:43:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.153	-	-
2015-09-03T11:06:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.305	-	-
2018-04-16T13:13:02	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.611	-	-
2019-06-24T09:36:08	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.22	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.236 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:	17.236 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		250	17.17
50000	5000000	292837502745264012667217	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-14T07:58:00	James Heinrich	Q6600	50000	5000000						3	0.206
2009-10-02T09:28:00	SubPrime	stor	50000	5000000						3	0.206
2010-08-06T21:39:00	James Classen	towerofart	50000	5000000						3	0.206
2011-12-18T05:36:00	Wojciech Florek	gafel	50000	5000000						3	0.206
2013-05-09T16:32:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-08T01:56:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-11-24T09:01:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-07-20T16:50:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-19T08:59:47	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-03-10T11:54:49	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-04-24T23:42:56	Bruce	DESK3	50000	5000000						3	0.206
2016-07-22T14:50:33	Bruce	DESK3	50000	5000000						3	0.206
2016-09-26T20:21:45	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-11-27T10:34:06	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-01-20T08:15:55	Bruce	DESK3	50000	5000000						3	0.206
2017-07-03T19:07:04	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-12-11T11:02:38	Bruce	DESK3	50000	5000000						3	0.206
2018-02-08T18:30:05	Bruce	DESK3	50000	5000000						3	0.206
2019-11-16T15:53:37	MichaelE	Zwoelfer	50000	5000000						3	0.206
2019-11-17T06:53:04	George Woltman	colab	50000	5000000						3	0.206
2019-11-18T10:58:34	mnd9	50871	50000	5000000						3	0.206
2019-11-22T17:28:47	wazuma	G751	50000	5000000						3	0.206
2019-11-24T07:28:56	J.R. Allen	lapacer	50000	5000000						3	0.206
2019-11-26T12:35:04	Sergey Nosov	TS140-02	50000	5000000						3	0.206
2019-11-29T18:32:50	Keysarecool	Boat_Anchor	50000	5000000	292837502745264012667217	77.954	1	2	2631934875075922	1	0.069
2020-06-01T14:17:23	TJAOI	Manual testing	50000	5000000						178	12.22

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	4EC7A534947EB720	0.094
2015-07-18T19:04:00	MadPoo	Manual testing	4EC7A534947EB720	0.094

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 = 2077640, B2 = 190924910 (P-1 stage 2)

B1 = 2077640, B2 = 173568100 (P-1 stage 2)

B1 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 2077640, B2 = 17356810 (P-1 stage 2)

B1 = 2077640 (P-1 stage 1)

B1 = 1888764 (P-1 stage 1)

B1 = 1717059 (P-1 stage 1)

B1 = 1560963 (P-1 stage 1)

B1 = 1419058 (P-1 stage 1)

B1 = 1290053 (P-1 stage 1)

B1 = 1172776 (P-1 stage 1)

B1 = 1066160 (P-1 stage 1)

B1 = 969237 (P-1 stage 1)

B1 = 881125 (P-1 stage 1)

B1 = 801023 (P-1 stage 1)

B1 = 728203 (P-1 stage 1)

B1 = 601821 (P-1 stage 1)

B1 = 497373 (P-1 stage 1)

B1 = 452158 (P-1 stage 1)

B1 = 411053 (P-1 stage 1)

B1 = 373685 (P-1 stage 1)

B1 = 280756 (P-1 stage 1)

B1 = 255233 (P-1 stage 1)

B1 = 210937 (P-1 stage 1)

B1 = 173958 (P-1 stage 1)

B1 = 95000, B2 = 1543750 (P-1 stage 2)

B1 = 136979 (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

10⁹

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