M2188349 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	27.2374	67.6471%	2500000	125000000	0.8746	7.9309%	28.1120	70.2129%	2.5659%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8603%	0.0194	63.1539%	1.0849%
GPU72	2⁶²	0.2807	64.5161%	11000	160000	0.0018	1.5699%	0.2826	65.0732%	0.5571%
Difference	+6	+26.9566	+3.1309%	+2489000	+124840000	+0.8728	+6.3609%	+27.8294	+5.1397%	+5.1397%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2188349	169945073284595318823089	24	77.169	38829517888736056 2³ × 59 × 82265927730373	2020-07-08	59	82265927730373	20,575	427,310	798,096

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.355%
2011-01-12T16:30:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.206%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	119330	119330		-		-	-	0.011	-	-	0.890%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148660	148660		-		-	-	0.014	-	-	1.007%
2016-02-13T08:02:49	Jocelyn Larouche	Manual testing	442473	4424730	6	-		-	-	0.063	-	-	3.588%
2018-02-22T23:12:20	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.931%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-03T00:34:00	Sturle Sunde	ginjtje.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T12:55:00	Sturle Sunde	fungo.ifi	2⁶¹	2⁶²		-	-	0.140	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.449	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.897	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.707	-	-
2016-01-02T13:51:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.415	-	-
2016-11-24T19:46:06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.830	-	-
2019-04-15T13:43:08	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.66	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.699 GHz-days
Estimated T-Level:	4.500

Digits	B1	Curves	Complete	FacMiss
20	11000	90 / 100	0.900	40.473%
25	50000	90 / 280	0.321	72.470%

New Calculation Method

Total ECM effort:	7.699 GHz-days
Estimated T-Level:	4.500

Digits	B1	Complete	FacMiss
20	11000	2.903	5.485%
25	50000	0.262	76.921%
30	250000	0.016	98.397%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		87	7.443
50000	5000000	169945073284595318823089	3	0.257

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-22T07:52:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.257
2009-12-11T03:43:00	James Hintz	ryan	50000	5000000						3	0.257
2011-09-03T01:38:00	Bud	annan	50000	5000000						3	0.257
2013-05-18T08:55:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-05T00:09:00	Jason U	Server7	50000	5000000						3	0.257
2015-12-12T07:32:13	guru	w1	50000	5000000						3	0.257
2016-03-11T19:05:45	Hartmut Birr	C7CE7B89E	50000	5000000						3	0.257
2016-06-26T20:54:30	Bruce	Desk6	50000	5000000						3	0.257
2016-11-03T23:49:34	Bruce	Desk6	50000	5000000						3	0.257
2017-04-15T23:12:06	Bruce	Desk6	50000	5000000						3	0.257
2017-11-04T11:26:42	Bruce	Desk6	50000	5000000						3	0.257
2018-03-18T16:50:43	Bruce	Desk6	50000	5000000						3	0.257
2018-09-11T13:36:52	Bruce	Desk6	50000	5000000						3	0.257
2020-01-29T20:52:40	Nesowa	6700T	50000	5000000						3	0.257
2020-02-08T03:33:52	Brett Walker	brain	50000	5000000						3	0.257
2020-02-15T12:31:44	Alvin Bunk	BADCAT	50000	5000000						3	0.257
2020-02-23T00:13:26	mnd9	75211backdoorb	50000	5000000						3	0.257
2020-03-04T03:31:06	mnd9	75201b	50000	5000000						3	0.257
2020-03-07T02:43:18	Alvin Bunk	BADCAT	50000	5000000						3	0.257
2020-03-14T05:40:02	mnd9	75201b	50000	5000000						3	0.257
2020-03-22T05:11:12	mnd9	libproj	50000	5000000						3	0.257
2020-04-03T12:46:17	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2020-04-17T05:46:34	daveward2005	Davy	50000	5000000						3	0.257
2020-04-26T10:14:53	nordi	sweet16	50000	5000000						3	0.257
2020-05-05T00:45:01	mnd9	27016b	50000	5000000						3	0.257
2020-05-17T02:19:40	mnd9	27016b	50000	5000000						3	0.257
2020-06-06T20:31:48	mnd9	25836b	50000	5000000						3	0.257
2020-06-22T19:23:29	GAN	KL-SCH04	50000	5000000						3	0.257
2020-07-01T18:36:55	IanGlencross	glenx24	50000	5000000						3	0.257
2020-07-08T21:29:40	mnd9	libproj	50000	5000000	169945073284595318823089	77.169	3	2	4254412963247095	3	0.257

date	userid	compid	res64	spent (GHz-days)
1997-12-30T00:00:00	ANONYMOUS	v4_computers	B697807BCEBF526A	0.144
1999-05-02T00:00:00	ANONYMOUS	v4_computers	B697807BCEBF526A	0.144
2018-04-14T17:03:04	kkmrkkblmbrbk	old	B697807BCEBF526A	0.144

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 442473, B2 = 4424730 (P-1 stage 2)

B1 = 442473 (P-1 stage 1)

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

B1 = 148660 (P-1 stage 1)

B1 = 119330 (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)

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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