M2494123 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	23.8981	67.6471%	3000000	100000000	0.8332	7.8768%	24.7314	70.1954%	2.5484%
PrimeNet	2⁵⁹	0.0308	62.7119%	10000	180000	0.0019	2.5368%	0.0327	63.6578%	0.9459%
GPU72	2⁶³	0.6399	65.0794%	11000	160000	0.0019	1.3814%	0.6418	65.5618%	0.4824%
Difference	+5	+23.2582	+2.5677%	+2989000	+99840000	+0.8313	+6.4954%	+24.0895	+4.6337%	+4.6337%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2494123	35358060186126819429211871	26	84.870	7088275154458464845 5 × 455557 × 3111915810517	2021-03-04	455557	3111915810517	1,817,346	17,052	31,848

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.235%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.786%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.263%
2011-01-24T19:38:00	Oscar Östlin		95000	1971250		-		-	-	0.020	-	-	2.387%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	120734	120734		-		-	-	0.012	-	-	0.917%
2014-12-04T13:39:00	mikr	MSI	2382500	85770100		-		-	-	0.697	-	-	7.552%
2015-12-26T08:48:51	mikr	MSI	3000000	100000000	12	-		-	-	0.833	-	-	7.877%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2016-02-23T16:29:15	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-10T21:12:00	Sturle Sunde	ginglo.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-11T11:06:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.123	-	-
2013-01-23T08:29:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.394	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.787	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.498	-	-
2015-10-31T16:44:06	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.996	-	-
2017-07-24T22:21:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.992	-	-
2019-04-08T13:40:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.98	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.569 GHz-days
Estimated T-Level:	22.054

Digits	B1	Curves	Complete	FacMiss
20	11000	115 / 100	1.150	31.481%
25	50000	115 / 280	0.411	66.269%

New Calculation Method

Total ECM effort:	10.569 GHz-days
Estimated T-Level:	22.054

Digits	B1	Complete	FacMiss
20	11000	3.710	2.449%
25	50000	0.335	71.514%
30	250000	0.021	97.957%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		108	9.93
50000	5000000	35358060186126819429211871	7	0.643

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-22T06:05:00	flying_pizza	bak1	50000	5000000						3	0.276
2010-04-01T13:57:00	James Classen	towerofart	50000	5000000						3	0.276
2012-07-11T02:38:00	soldake	PentiumD	50000	5000000						3	0.276
2014-02-18T22:53:00	Andy Incline	Office-PC	50000	5000000						3	0.276
2015-07-24T18:38:00	nranks	wlaptop	50000	5000000						3	0.276
2016-02-27T01:00:49	arnaud	CHAMOT09	50000	5000000						3	0.276
2016-06-25T15:50:27	Jason U	Server7	50000	5000000						3	0.276
2017-03-22T20:07:55	deo2016	deo2016.home.new	50000	5000000						3	0.276
2017-08-16T20:01:34	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2017-12-28T20:12:33	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2018-08-21T09:23:08	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2019-10-21T07:13:13	monsted	rootweiler	50000	5000000						3	0.276
2020-05-17T11:41:06	mnd9	25836b	50000	5000000						3	0.276
2020-06-04T23:46:13	Nesowa	6700T	50000	5000000						3	0.276
2020-06-23T09:46:03	LaurV	3tits	50000	5000000						3	0.276
2020-07-02T02:02:35	GAN	LMS-12	50000	5000000						3	0.276
2020-07-08T20:45:28	daveward2005	Davy	50000	5000000						3	0.276
2020-07-15T06:03:53	mnd9	25836b	50000	5000000						3	0.276
2020-07-20T21:45:34	Ahmed Azhad	c5.large.az	50000	5000000						3	0.276
2020-07-27T10:12:59	daveward2005	Dave2	50000	5000000						3	0.276
2020-08-03T15:59:31	GAN	LMS-17	50000	5000000						3	0.276
2020-08-11T13:11:37	GAN	LMS-01	50000	5000000						3	0.276
2020-08-28T14:41:24	M. R. Mayer	nimbus	50000	5000000						7	0.643
2020-10-01T20:20:27	daveward2005	Dave2	50000	5000000						7	0.643
2020-10-29T00:00:18	Nesowa	6700T	50000	5000000						7	0.643
2020-12-02T07:44:31	lycorn	colab_S_1	50000	5000000						7	0.643
2021-01-05T00:03:59	IanGlencross	glenx24	50000	5000000						7	0.643
2021-02-04T06:43:23	Zenzoma	AMD3970X	50000	5000000						7	0.643
2021-03-04T21:45:28	mnd9	75211backdoor	50000	5000000	35358060186126819429211871	84.870	7	2	6214817061171385	7	0.643

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	CD5D5E9F1A16F5DA	0.173
2018-06-01T08:53:32	kkmrkkblmbrbk	old	CD5D5E9F1A16F5DA	0.173

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 2382500, B2 = 85770100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2382500 (P-1 stage 1)

B1 = 95000, B2 = 1971250 (P-1 stage 2)

B1 = 120734 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (P-1 stage 2)

B1 = 20000 (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

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