M2174269 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	2⁶⁸	27.4138	67.6471%	5000000	200000000	1.4896	8.9472%	28.9033	70.5418%	2.8947%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8569%	0.0195	63.1526%	1.0836%
GPU72	2⁶²	0.2826	64.5161%	11000	160000	0.0018	1.5679%	0.2844	65.0725%	0.5564%
Difference	+6	+27.1312	+3.1309%	+4989000	+199840000	+1.4877	+7.3793%	+28.6189	+5.4693%	+5.4693%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2174269	2103819093139133309031198577	28	90.765	483799174145226121752 2³ × 3⁴ × 293 × 2764123 × 921860341	2020-06-11	2764123	921860341	141,083,639	5.0375	8.9433

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-05T01:17:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-07T21:16:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.354%
2011-01-15T13:00:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.203%
2014-06-13T02:40:00	Jocelyn Larouche	Manual testing	119520	119520		-		-	-	0.011	-	-	0.889%
2014-10-05T22:22:00	Jocelyn Larouche	Manual testing	149040	149040		-		-	-	0.014	-	-	1.007%
2015-12-20T13:06:10	HBendtz	Manual testing	700000	21000000	12	-		-	-	0.172	-	-	5.204%
2019-11-13T19:58:09	mikr	MSI	5000000	200000000	12	-		-	-	1.490	-	-	8.947%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-04T18:57:00	Sturle Sunde	gorro.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-07T11:25:00	Sturle Sunde	wright.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.451	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.903	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.718	-	-
2016-01-02T13:50:57	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.437	-	-
2016-11-17T17:00:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.874	-	-
2019-04-29T13:20:33	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.180 GHz-days
Estimated T-Level:	4.200

Digits	B1	Curves	Complete	FacMiss
20	11000	84 / 100	0.840	42.989%
25	50000	84 / 280	0.300	74.042%

New Calculation Method

Total ECM effort:	7.180 GHz-days
Estimated T-Level:	4.200

Digits	B1	Complete	FacMiss
20	11000	2.710	6.656%
25	50000	0.245	78.278%
30	250000	0.015	98.503%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		81	6.924
50000	5000000	2103819093139133309031198577	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T07:23:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.256
2009-12-07T14:50:00	Piepen	T41-2000	50000	5000000						3	0.256
2011-08-30T05:10:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.256
2013-05-11T19:03:00	Xyzzy	J	50000	5000000						3	0.256
2015-02-22T00:12:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2015-10-29T22:54:38	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2016-03-04T15:42:13	Jason U	Server7	50000	5000000						3	0.256
2016-06-22T13:01:06	lettp	Home	50000	5000000						3	0.256
2016-10-19T21:43:27	Bruce	Desk6	50000	5000000						3	0.256
2017-04-03T16:49:24	Bruce	Desk6	50000	5000000						3	0.256
2017-10-30T07:38:05	Conductor	Sasha	50000	5000000						3	0.256
2018-03-07T20:57:28	Bruce	Desk6	50000	5000000						3	0.256
2018-08-20T16:23:58	-Anonymous-	Kitchen	50000	5000000						3	0.256
2020-01-24T11:16:09	George Woltman	colab	50000	5000000						3	0.256
2020-02-02T04:11:25	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-02-11T20:58:23	Nesowa	entropy_generator_2	50000	5000000						3	0.256
2020-02-17T22:11:28	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-02-25T13:47:15	cappy95833	HomePC	50000	5000000						3	0.256
2020-03-02T22:51:26	Nesowa	6700T	50000	5000000						3	0.256
2020-03-09T20:37:57	Nesowa	6700T	50000	5000000						3	0.256
2020-03-17T06:48:43	kracker	O0	50000	5000000						3	0.256
2020-03-27T06:51:12	kracker	O0	50000	5000000						3	0.256
2020-04-07T22:39:55	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-04-21T07:36:34	mnd9	l2lounge	50000	5000000						3	0.256
2020-04-28T19:33:36	mnd9	fb	50000	5000000						3	0.256
2020-05-09T06:48:08	Greg Hogan	azure4	50000	5000000						3	0.256
2020-05-23T08:36:44	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-06-11T13:56:51	mnd9	25836b	50000	5000000	2103819093139133309031198577	90.765	3	2	4235820477275057	3	0.256

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	5C7B305C9465C55E	0.143
2018-04-12T15:39:35	kkmrkkblmbrbk	old	5C7B305C9465C55E	0.143

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 700000, B2 = 21000000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 149040 (P-1 stage 1)

B1 = 119520 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (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

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