M1724413 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	17.2313	68.6567%	3642200	123456789	0.6940	8.6234%	17.9253	71.3596%	2.7028%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0010	2.7947%	0.0122	64.1875%	1.0296%
GPU72	2⁶¹	0.1781	65.5738%	7000	110000	0.0009	1.3444%	0.1790	66.0366%	0.4628%
Difference	+6	+17.0532	+3.0829%	+3635200	+123346789	+0.6931	+7.2790%	+17.7463	+5.3230%	+5.3230%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1724413	229200703495926172965550073743	30	97.533	66457601368096324072467 3 × 11 × 17 × 223 × 701 × 2819 × 3643 × 73791217	2015-08-28	3643	73791217	2.114e+10	0.2746	0.5124

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:49:00	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%
2014-10-01T22:53:00	Jocelyn Larouche	Manual testing	187221	187221		-		-	-	0.013	-	-	1.248%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	280831	280831		-		-	-	0.019	-	-	1.525%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	373785	373785		-		-	-	0.026	-	-	1.741%
2015-02-22T09:50:00	Jocelyn Larouche	Manual testing	411163	411163		-		-	-	0.028	-	-	1.816%
2015-03-06T12:09:00	Jocelyn Larouche	Manual testing	452279	452279		-		-	-	0.031	-	-	1.894%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	497506	497506		-		-	-	0.034	-	-	1.973%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	601981	601981		-		-	-	0.041	-	-	2.137%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	728396	728396		-		-	-	0.050	-	-	2.309%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	801235	801235		-		-	-	0.055	-	-	2.397%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	881358	881358		-		-	-	0.060	-	-	2.488%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	969493	969493		-		-	-	0.066	-	-	2.580%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1066442	1066442		-		-	-	0.073	-	-	2.674%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1173086	1173086		-		-	-	0.080	-	-	2.770%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1290394	1290394		-		-	-	0.088	-	-	2.867%
2015-07-21T01:19:00	Jocelyn Larouche	Manual testing	1419433	1419433		-		-	-	0.097	-	-	2.967%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1561376	1561376		-		-	-	0.107	-	-	3.068%
2015-08-28T09:45:00	mikr	MSI	3642200	123456789	12		229200703495926172965550073743	30	97.533	0.694	0.162	1.388	8.623%

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	-	-
2010-04-24T18:40:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.089	-	-
2010-10-27T20:37:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.926	-	-
2015-05-04T00:34:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.139	-	-
2015-05-04T00:34:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.167	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.121 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	15.121 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		254	15.12

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-07T12:25:00	paulie	iMac3.4	50000	5000000						3	0.179
2009-09-27T12:25:00	ekrumme	nuanceH2	50000	5000000						3	0.179
2009-09-27T13:42:00	ekrumme	nuanceH2	50000	5000000						3	0.179
2009-09-27T14:51:00	ekrumme	nuanceH2	50000	5000000						3	0.179
2013-04-29T23:19:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-01-28T12:39:00	Sara	Sara	50000	5000000						3	0.179
2014-11-02T06:01:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2015-07-04T03:45:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2020-05-08T02:29:35	Oliver Kruse	IOS-2	50000	5000000						3	0.179
2020-05-18T10:37:47	TJAOI	Manual testing	50000	5000000						227	13.51

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	Dry Creek Photo	v4_computers	6D5D5B97EADC3E25	0.081
2015-07-03T04:32:00	MadPoo	Manual testing	6D5D5B97EADC3E25	0.081

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 = 1561376 (P-1 stage 1)

B1 = 1419433 (P-1 stage 1)

B1 = 1290394 (P-1 stage 1)

B1 = 1173086 (P-1 stage 1)

B1 = 1066442 (P-1 stage 1)

B1 = 969493 (P-1 stage 1)

B1 = 881358 (P-1 stage 1)

B1 = 801235 (P-1 stage 1)

B1 = 728396 (P-1 stage 1)

B1 = 601981 (P-1 stage 1)

B1 = 497506 (P-1 stage 1)

B1 = 452279 (P-1 stage 1)

B1 = 411163 (P-1 stage 1)

B1 = 373785 (P-1 stage 1)

B1 = 280831 (P-1 stage 1)

B1 = 187221 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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