M1735549 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	17.1208	68.6567%	3642200	123456789	0.8000	8.6287%	17.9208	71.3612%	2.7045%
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%	0.1781	66.0593%	0.4855%
Difference	+6	+16.9438	+3.0829%	+3634200	+123346789	+0.7989	+7.2185%	+17.7427	+5.3020%	+5.3020%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1735549	53556160686283552724666537	26	85.469	15429169872554319332 2² × 11 × 1621 × 17807 × 12148316849	2016-03-10	17807	12148316849	8,943,694	52.066	97.242

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-11T06:19:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.399%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.886%
2014-05-06T10:52:00	Jocelyn Larouche	Manual testing	136982	136982		-		-	-	0.011	-	-	1.059%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	173964	173964		-		-	-	0.014	-	-	1.203%
2014-12-02T21:55:00	Jocelyn Larouche	Manual testing	210946	210946		-		-	-	0.017	-	-	1.328%
2015-01-27T21:58:00	Jocelyn Larouche	Manual testing	255244	255244		-		-	-	0.020	-	-	1.458%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	280768	280768		-		-	-	0.022	-	-	1.527%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	373700	373700		-		-	-	0.029	-	-	1.742%
2015-02-21T13:42:00	Jocelyn Larouche	Manual testing	411070	411070		-		-	-	0.032	-	-	1.818%
2015-03-08T04:50:00	Jocelyn Larouche	Manual testing	452177	452177		-		-	-	0.036	-	-	1.895%
2015-03-15T18:55:00	Jocelyn Larouche	Manual testing	497394	497394		-		-	-	0.039	-	-	1.975%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	601846	601846		-		-	-	0.047	-	-	2.139%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	728233	728233		-		-	-	0.057	-	-	2.311%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	801056	801056		-		-	-	0.063	-	-	2.399%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	881161	881161		-		-	-	0.069	-	-	2.490%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	969277	969277		-		-	-	0.076	-	-	2.582%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1066204	1066204		-		-	-	0.084	-	-	2.676%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1172824	1172824		-		-	-	0.092	-	-	2.772%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1290106	1290106		-		-	-	0.101	-	-	2.870%
2015-07-21T01:20:00	Jocelyn Larouche	Manual testing	1419116	1419116		-		-	-	0.112	-	-	2.969%
2015-07-27T01:26:00	Jocelyn Larouche	Manual testing	1561027	1561027		-		-	-	0.123	-	-	3.071%
2015-09-16T07:26:00	Jocelyn Larouche	Manual testing	1717129	1717129		-		-	-	0.135	-	-	3.174%
2015-09-27T21:23:22	Jocelyn Larouche	Manual testing	1888841	1888841		-		-	-	0.149	-	-	3.279%
2015-09-28T03:52:31	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	8.629%

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	-	-
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	-	-
2010-04-22T12:45:00	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		-	-	4.306	-	-

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		248	17.03
50000	5000000	53556160686283552724666537	3	0.206

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-13T13:19:00	Team_Bundu	bundu4	50000	5000000						3	0.206
2009-10-02T03:08:00	SubPrime	stor	50000	5000000						3	0.206
2010-08-07T17:44:00	Kamil_Górski	thefault	50000	5000000						3	0.206
2011-12-20T11:58:00	OS1	L3	50000	5000000						3	0.206
2013-05-09T13:33:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-07T22:06:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-11-24T05:03:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-07-20T12:41:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-19T06:22:03	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-03-10T10:53:55	Chang Chia-Tche	exbpc13	50000	5000000	53556160686283552724666537	85.469	3	2		3	0.206
2020-05-25T09:37:50	TJAOI	Manual testing	50000	5000000						221	15.18

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	790C739B74529444	0.094
2015-06-29T14:43:00	MadPoo	Manual testing	790C739B74529444	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 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 1888841 (P-1 stage 1)

B1 = 1717129 (P-1 stage 1)

B1 = 1561027 (P-1 stage 1)

B1 = 1419116 (P-1 stage 1)

B1 = 1290106 (P-1 stage 1)

B1 = 1172824 (P-1 stage 1)

B1 = 1066204 (P-1 stage 1)

B1 = 969277 (P-1 stage 1)

B1 = 881161 (P-1 stage 1)

B1 = 801056 (P-1 stage 1)

B1 = 728233 (P-1 stage 1)

B1 = 601846 (P-1 stage 1)

B1 = 497394 (P-1 stage 1)

B1 = 452177 (P-1 stage 1)

B1 = 411070 (P-1 stage 1)

B1 = 373700 (P-1 stage 1)

B1 = 280768 (P-1 stage 1)

B1 = 255244 (P-1 stage 1)

B1 = 210946 (P-1 stage 1)

B1 = 173964 (P-1 stage 1)

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

B1 = 136982 (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

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