M2078627 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	14.2950	68.6567%	2246492	8985968	0.2492	5.2327%	14.5442	70.2968%	1.6401%
PrimeNet	2⁵⁸	0.0185	63.7931%	9000	160000	0.0016	2.6726%	0.0201	64.7608%	0.9677%
GPU72	2⁶²	0.2956	66.1290%	9000	130000	0.0015	1.3675%	0.2970	66.5922%	0.4632%
Difference	+5	+13.9994	+2.5277%	+2237492	+8855968	+0.2477	+3.8651%	+14.2471	+3.7046%	+3.7046%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2078627	109903888978260024628699129	27	86.506	26436654815476760532 2² × 3⁴ × 149 × 2467 × 221976026171	2017-07-26	2467	221976026171	13,923,297	1,153.0	2,153.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.276%
2009-07-25T14:54:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.018%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.414%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.595%
2011-01-21T10:13:00	James Heinrich	Q6600	135000	3105000		-		-	-	0.028	-	-	3.096%
2014-11-12T02:17:00	Jocelyn Larouche	Manual testing	165878	165878		-		-	-	0.016	-	-	1.210%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	207347	207347		-		-	-	0.020	-	-	1.357%
2015-01-30T21:42:00	Jocelyn Larouche	Manual testing	228081	228081		-		-	-	0.022	-	-	1.422%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	250889	250889		-		-	-	0.024	-	-	1.490%
2015-02-02T07:32:00	Jocelyn Larouche	Manual testing	275977	275977		-		-	-	0.026	-	-	1.559%
2015-02-12T12:33:00	Jocelyn Larouche	Manual testing	444461	444461		-		-	-	0.042	-	-	1.933%
2015-02-14T12:30:00	Jocelyn Larouche	Manual testing	537797	537797		-		-	-	0.051	-	-	2.096%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	591576	591576		-		-	-	0.056	-	-	2.181%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	650733	650733		-		-	-	0.062	-	-	2.267%
2015-03-03T20:46:00	Jocelyn Larouche	Manual testing	715806	715806		-		-	-	0.068	-	-	2.355%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	787386	787386		-		-	-	0.075	-	-	2.445%
2015-03-15T18:55:00	Jocelyn Larouche	Manual testing	866124	866124		-		-	-	0.083	-	-	2.536%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	1048009	1048009		-		-	-	0.100	-	-	2.725%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	1268089	1268089		-		-	-	0.121	-	-	2.921%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	1394897	1394897		-		-	-	0.133	-	-	3.022%
2015-05-22T00:29:00	Jocelyn Larouche	Manual testing	1534386	1534386		-		-	-	0.146	-	-	3.125%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	1687824	1687824		-		-	-	0.161	-	-	3.229%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1856606	1856606		-		-	-	0.177	-	-	3.336%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	2042266	2042266		-		-	-	0.195	-	-	3.444%
2015-07-07T18:14:00	Jocelyn Larouche	Manual testing	2246492	2246492		-		-	-	0.214	-	-	3.554%
2016-07-07T00:37:34	Jocelyn Larouche	Manual testing	2246492	4492984	6	-		-	-	0.226	-	-	4.390%
2016-09-26T02:47:45	Jocelyn Larouche	low 4M	2246492	8985968	6	-		-	-	0.249	-	-	5.233%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	Stephen Wood	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T07:30:00	Sturle Sunde	hummel.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-17T09:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.148	-	-
2013-09-02T08:36:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.472	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.945	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.798	-	-
2015-11-05T09:47:17	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.595	-	-
2016-09-12T00:05:07	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.190	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.635 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	2.635 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.090	91.358%
30	250000	0.006	99.445%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.550
50000	5000000	109903888978260024628699129	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-17T22:24:00	ClknGo Software	plms3	50000	5000000						3	0.255
2009-11-03T00:25:00	SubPrime	stor	50000	5000000						3	0.255
2011-05-18T06:10:00	Beat Bucheli	I7	50000	5000000						3	0.255
2013-03-16T14:08:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-08-17T15:52:00	arnaud	SPR05	50000	5000000						3	0.255
2015-07-24T09:17:00	guru	w1	50000	5000000						3	0.255
2016-02-20T02:49:43	Sintax	cloud2	50000	5000000						3	0.255
2016-05-15T16:54:21	Bruce	Desk6	50000	5000000						3	0.255
2016-07-25T12:04:32	Bruce	test	50000	5000000						3	0.255
2017-01-08T09:35:34	Bruce	Desk6	50000	5000000						3	0.255
2017-07-26T06:05:28	Bruce	Desk6	50000	5000000	109903888978260024628699129	86.506	1	2		1	0.085

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	Stephen Wood	v4_computers	FF7112E0EA2D0959	0.137
2017-06-06T09:42:52	kkmrkkblmbrbk	c4.large	FF7112E0EA2D0959	0.137

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 = 2246492, B2 = 8985968 (P-1 stage 2)

B1 = 2246492, B2 = 4492984 (P-1 stage 2)

B1 = 2246492 (P-1 stage 1)

B1 = 2042266 (P-1 stage 1)

B1 = 1856606 (P-1 stage 1)

B1 = 1687824 (P-1 stage 1)

B1 = 1534386 (P-1 stage 1)

B1 = 1394897 (P-1 stage 1)

B1 = 1268089 (P-1 stage 1)

B1 = 1048009 (P-1 stage 1)

B1 = 866124 (P-1 stage 1)

B1 = 787386 (P-1 stage 1)

B1 = 715806 (P-1 stage 1)

B1 = 650733 (P-1 stage 1)

B1 = 591576 (P-1 stage 1)

B1 = 537797 (P-1 stage 1)

B1 = 444461 (P-1 stage 1)

B1 = 135000, B2 = 3105000 (P-1 stage 2)

B1 = 275977 (P-1 stage 1)

B1 = 250889 (P-1 stage 1)

B1 = 228081 (P-1 stage 1)

B1 = 207347 (P-1 stage 1)

B1 = 165878 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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