M1678753 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	17.7000	68.6567%	1000000	20000000	0.1389	5.6990%	17.8389	70.4430%	1.7862%
PrimeNet	2⁵⁷	0.0114	63.1579%	8000	130000	0.0010	2.7248%	0.0124	64.1618%	1.0039%
GPU72	2⁶¹	0.1830	65.5738%	7000	90000	0.0008	1.2552%	0.1838	66.0059%	0.4321%
Difference	+6	+17.5170	+3.0829%	+993000	+19910000	+0.1381	+4.4437%	+17.6551	+4.4371%	+4.4371%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1678753	83755812077050438392631	23	76.149	24945841370663355 3 × 5 × 941 × 1767328471177	2017-09-30	941	1767328471177	16,842	6,570.8	12,272

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-24T01:11:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.569%
2012-02-29T17:10:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.881%
2012-02-29T17:14:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.285%
2012-02-29T18:10:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.567%
2012-02-29T18:13:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.787%
2012-02-29T19:11:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.969%
2012-02-29T19:13:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	2.126%
2012-02-29T20:10:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.264%
2012-02-29T20:13:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.387%
2012-02-29T21:11:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.498%
2012-02-29T21:14:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.601%
2012-03-01T06:09:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.732%
2012-03-01T07:10:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.699%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:45	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.069	-	-
2010-04-27T19:20:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.091	-	-
2016-02-23T16:28:45	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.183	-	-
2010-09-13T18:09:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.951	-	-
2016-02-23T16:28:45	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.585	-	-
2015-05-13T07:35:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.170	-	-
2015-05-14T02:07:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.226	-	-
2015-10-11T16:52:35	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.451	-	-
2017-09-22T15:53:15	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.903	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.900 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:	14.900 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	14.72
50000	5000000	83755812077050438392631	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-10T09:49:00	Scott Kurowski	LM-Dell4600	50000	5000000						3	0.178
2009-09-18T16:11:00	SubPrime	stor	50000	5000000						3	0.178
2010-06-06T22:14:00	James Hintz	ryan	50000	5000000						3	0.178
2011-11-11T16:58:00	Lukasz Wrobel	i-1	50000	5000000						3	0.178
2013-04-01T05:30:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2013-12-19T07:43:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-08-14T06:17:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-11-25T02:19:00	mikr	MSI	50000	5000000						12	0.712
2016-05-27T05:17:56	Bruce	DESK3	50000	5000000						3	0.178
2016-08-22T10:41:12	Bruce	DESK3	50000	5000000						3	0.178
2016-10-25T08:12:26	Bruce	DESK3	50000	5000000						3	0.178
2016-12-23T03:21:44	Bruce	DESK3	50000	5000000						3	0.178
2017-04-11T01:29:51	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-09-30T17:17:52	Chang Chia-Tche	exbpc13	50000	5000000	83755812077050438392631	76.149	3	2		3	0.178
2020-01-06T12:25:34	TJAOI	Manual testing	50000	5000000						200	11.87

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	1B6EA8BE232CE1AA	0.079
2016-06-02T10:52:44	MadPoo	Manual testing	1B6EA8BE232CE1AA	0.079

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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