M1709233 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	17.3844	68.6567%	3642200	123456789	0.6940	8.6161%	18.0784	71.3573%	2.7006%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7900%	0.0123	64.1858%	1.0279%
GPU72	2⁶¹	0.1797	65.5738%	7000	100000	0.0008	1.3028%	0.1805	66.0223%	0.4485%
Difference	+6	+17.2046	+3.0829%	+3635200	+123356789	+0.6932	+7.3133%	+17.8978	+5.3350%	+5.3350%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1709233	2354208494939586761460738802721	31	100.893	688673953445664447579920 2⁴ × 5 × 7 × 43 × 107 × 11483 × 3008429 × 7737101	2015-07-28	3008429	7737101	7.625e+10	0.2229	0.4178

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-20T00:00:00	Jocelyn Larouche	v4_computers	25000	356250		-		-	-	0.003	-	-	1.157%
2011-02-11T06:20:00	Carsten Kossendey	leela	90000	1507500		-		-	-	0.011	-	-	2.354%
2014-03-31T21:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.884%
2014-04-29T21:12:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.010	-	-	1.109%
2014-10-05T22:25:00	Jocelyn Larouche	Manual testing	187551	187551		-		-	-	0.013	-	-	1.247%
2015-01-07T04:02:00	Jocelyn Larouche	Manual testing	281326	281326		-		-	-	0.019	-	-	1.524%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	309458	309458		-		-	-	0.021	-	-	1.594%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	374443	374443		-		-	-	0.026	-	-	1.740%
2015-02-23T15:50:00	Jocelyn Larouche	Manual testing	411887	411887		-		-	-	0.028	-	-	1.815%
2015-03-05T14:27:00	Jocelyn Larouche	Manual testing	453075	453075		-		-	-	0.031	-	-	1.893%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	498382	498382		-		-	-	0.034	-	-	1.972%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	603042	603042		-		-	-	0.041	-	-	2.136%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	729680	729680		-		-	-	0.050	-	-	2.307%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	802648	802648		-		-	-	0.055	-	-	2.396%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	882912	882912		-		-	-	0.060	-	-	2.486%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	971203	971203		-		-	-	0.066	-	-	2.578%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1068323	1068323		-		-	-	0.073	-	-	2.672%
2015-06-25T21:14:00	Jocelyn Larouche	Manual testing	1175155	1175155		-		-	-	0.080	-	-	2.768%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1292670	1292670		-		-	-	0.088	-	-	2.866%
2015-07-13T12:24:00	Jocelyn Larouche	Manual testing	1421937	1421937		-		-	-	0.097	-	-	2.965%
2015-07-21T01:20:00	Jocelyn Larouche	Manual testing	1564130	1564130		-		-	-	0.107	-	-	3.067%
2015-07-28T02:05:00	mikr	MSI	3642200	123456789	12		2354208494939586761460738802721	31	100.893	0.694	0.161	1.388	8.616%

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	-	-
2022-03-08T23:06:23	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2010-04-24T12:42:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.090	-	-
2010-10-16T22:16:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.934	-	-
2015-04-28T06:34:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.149	-	-
2015-04-28T06:34:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.186	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.928 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:	14.928 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		251	14.93

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-27T11:49:00	Team_Bundu	bundu4	50000	5000000						3	0.178
2009-06-21T01:58:00	James Hintz	02_060209	50000	5000000						3	0.178
2010-07-10T02:09:00	unconnected	X3220--xp	50000	5000000						3	0.178
2011-11-23T14:54:00	Bud	annan	50000	5000000						3	0.178
2013-04-25T16:31:00	OS1	L3	50000	5000000						3	0.178
2014-01-12T03:05:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-10-08T23:13:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2015-06-08T19:22:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-03-16T11:29:56	TJAOI	Manual testing	50000	5000000						227	13.50

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	45EF363F8E1EDD2B	0.080
2015-06-27T00:57:00	MadPoo	Manual testing	45EF363F8E1EDD2B	0.080

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 = 1564130 (P-1 stage 1)

B1 = 1421937 (P-1 stage 1)

B1 = 1292670 (P-1 stage 1)

B1 = 1175155 (P-1 stage 1)

B1 = 1068323 (P-1 stage 1)

B1 = 971203 (P-1 stage 1)

B1 = 882912 (P-1 stage 1)

B1 = 802648 (P-1 stage 1)

B1 = 729680 (P-1 stage 1)

B1 = 603042 (P-1 stage 1)

B1 = 498382 (P-1 stage 1)

B1 = 453075 (P-1 stage 1)

B1 = 411887 (P-1 stage 1)

B1 = 374443 (P-1 stage 1)

B1 = 309458 (P-1 stage 1)

B1 = 281326 (P-1 stage 1)

B1 = 187551 (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)

B1 = 25000, B2 = 356250 (P-1 stage 2)

B1 = 25000 (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