M1233709 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	2⁷¹	387.5130	70.4225%	200000000	2000300838690	4,854.4710	21.0647%	5,241.9840	76.6529%	6.2304%
Target	2⁶⁰	0.1245	65.0000%	5000	30000	0.0003	0.8311%	0.1248	65.2909%	0.2909%
Difference	+11	+387.3885	+5.4225%	+199995000	+2000300808690	+4,854.4707	+20.2336%	+5,241.8592	+11.3621%	+5.9395%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1233709	699914176996038857447523120648402454952401	42	139.006	283662588582898745752654443085201800 2³ × 3 × 5² × 11 × 97 × 173 × 227 × 389 × 75679 × 192759563 × 1988261543	2023-01-18	192759563	1988261543	1.264e+11	12.921	17.444

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-10-07T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.44667e-5	-	-	0.002%
2002-12-25T00:00:00	ANONYMOUS	v4_computers	20000	395000		-		-	-	0.002	-	-	0.563%
2013-10-25T07:49:00	David Campeau	i5-2500k	1325000	33125000		-		-	-	0.136	-	-	4.308%
2016-08-03T10:15:52	Bruno Victal	5820K-factoring	2500000	62500000	12	-		-	-	0.257	-	-	5.171%
2016-08-27T10:52:59	Bruno Victal	Manual testing	2500000	62500000	12	-		-	-	0.257	-	-	5.171%
2018-05-01T11:52:40	Jocelyn Larouche	low 4M	1233709	123370900	12	-		-	-	0.351	-	-	5.353%
2018-10-13T20:38:14	Jocelyn Larouche	low 4M	1233709	135707990	12	-		-	-	0.381	-	-	5.433%
2022-05-29T15:29:01	Sid & Andy	Barrel_Of_Monkeys	25000000	128252050290		-		-	-	311.8	-	-	15.517%
2023-01-18T10:52:20	kracker	reflection	200000000	2000300838690			699914176996038857447523120648402454952401	42	139.006	4,854	0.076	9,709	21.065%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.016	-	-
2003-05-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.031	-	-
2016-02-23T16:28:25	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.093	-	-
2009-02-17T20:52:00	Sturle Sunde	fungo.ifi	2⁶⁰	2⁶¹		-	-	0.124	-	-
2012-09-14T10:24:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.249	-	-
2012-10-26T08:03:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.796	-	-
2015-04-02T13:10:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.591	-	-
2015-04-06T10:49:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	3.029	-	-
2015-09-20T20:58:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	6.057	-	-
2018-07-17T00:12:10	ramgeis	Manual testing	2⁶⁶	2⁶⁷		-	-	12.11	-	-
2018-07-17T00:12:10	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	24.23	-	-
2020-10-20T01:05:02	kracker	Manual testing	2⁶⁸	2⁶⁹		-	-	48.46	-	-
2020-10-20T20:39:08	kracker	Manual testing	2⁶⁹	2⁷⁰		-	-	96.91	-	-
2020-10-24T13:26:08	kracker	Manual testing	2⁷⁰	2⁷¹		-	-	193.8	-	-

ECM factoring results:

Total ECM effort:	18.551 GHz-days
Estimated T-Level:	25.658

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	10.40
250000	25000000		44	8.146

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-06T17:39:00	Chad Davis	Bayes	50000	5000000						1	0.037
2008-08-20T23:12:00	Sturle Sunde	v21	50000	5000000						3	0.111
2009-02-02T16:21:00	Sturle Sunde	v21	50000	5000000						3	0.111
2009-06-27T10:43:00	Lupo	yorick	50000	5000000						3	0.111
2009-10-08T12:05:00	James Hintz	jeff4	50000	5000000						3	0.111
2010-03-02T06:10:00	Geoff Wing	GW1	50000	5000000						3	0.111
2010-11-24T20:04:00	greensinoz	giopa01	50000	5000000						3	0.111
2011-08-27T14:27:00	Bruce	GTLT-4540GZ	50000	5000000						3	0.111
2012-05-10T12:32:00	OS1	Tina	50000	5000000						3	0.111
2012-10-19T14:20:00	OS1	Tina	50000	5000000						3	0.111
2013-07-30T12:01:00	OS1	Tina	50000	5000000						3	0.111
2014-01-16T15:01:00	jim f in mn	asus	50000	5000000						3	0.111
2014-03-07T22:20:00	Bruce	xps630	50000	5000000						3	0.111
2014-07-24T19:19:00	OS1	Tina	50000	5000000						3	0.111
2015-03-06T14:32:00	Jason U	Dell-Win7	50000	5000000						3	0.111
2015-05-23T16:36:00	Jason U	Dell-Win7	50000	5000000						3	0.111
2015-09-20T17:45:00	Jason U	Dell-Win7	50000	5000000						3	0.111
2015-12-22T22:37:57	arnaud	CHAMOT06	50000	5000000						3	0.111
2016-03-10T16:58:03	arnaud	CHAMOT06	50000	5000000						3	0.111
2016-04-11T09:16:20	raman22feb1988	Vijay	50000	5000000						3	0.111
2016-05-08T22:17:04	Jason U	Dell-Win7	50000	5000000						3	0.111
2016-06-24T15:45:28	raman22feb1988	Santhosh	50000	5000000						3	0.111
2016-09-09T03:37:35	Bruce	Desk9	50000	5000000						3	0.111
2016-11-10T00:41:09	thelegendarymudkip	Manual testing	50000	5000000						5	0.185
2017-09-07T15:04:14	hiner112	girls	50000	5000000						3	0.111
2017-11-24T16:12:49	TJAOI	Manual testing	50000	5000000						65	2.407
2018-09-28T10:42:43	TJAOI	Manual testing	50000	5000000						141	5.221
2021-03-12T16:32:12	TJAOI	Manual testing	250000	25000000						44	8.146

date	userid	compid	res64	spent (GHz-days)
2015-11-12T20:09:37	MadPoo	Manual testing	01974EA6189BC0E0	0.038

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 = 200000000, B2 = 2000300838690 (P-1 stage 2)

B1 = 25000000, B2 = 128252050290 (P-1 stage 2)

B1 = 200000000 (P-1 stage 1)

B1 = 25000000 (P-1 stage 1)

B1 = 1233709, B2 = 135707990 (P-1 stage 2)

B1 = 1233709, B2 = 123370900 (P-1 stage 2)

B1 = 2500000, B2 = 62500000 (P-1 stage 2)

B1 = 1325000, B2 = 33125000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 1325000 (P-1 stage 1)

B1 = 1233709 (P-1 stage 1)

B1 = 20000, B2 = 395000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10²

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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