M1030349 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	463.9965	71.8310%	28000000	85350951840	200.9847	14.9439%	664.9811	76.0405%	4.2096%
PrimeNet	2⁵⁶	0.0093	64.2857%	4500	60000	0.0003	1.9511%	0.0096	64.9825%	0.6968%
GPU72	2⁶⁰	0.1491	66.6667%	4500	18000	0.0002	0.6148%	0.1493	66.8716%	0.2049%
Difference	+11	+463.8474	+5.1643%	+27995500	+85350933840	+200.9844	+14.3291%	+664.8318	+9.1689%	+9.1689%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-22T00:00:00	Jocelyn Larouche	v4_computers	10000	117500		-		-	-	0.001	-	-	0.259%
2002-11-09T00:00:00	Jocelyn Larouche	v4_computers	11000	11000		-		-	-	0.000	-	-	0.067%
2002-11-09T00:00:00	Jocelyn Larouche	v4_computers	15000	15000		-		-	-	0.001	-	-	0.094%
2002-11-16T00:00:00	Jocelyn Larouche	v4_computers	20000	20000		-		-	-	0.001	-	-	0.124%
2012-01-02T19:32:00	bcp19	Toshiba-740Q	200000	10000000		-		-	-	0.032	-	-	2.468%
2012-02-23T08:03:00	bcp19	Toshiba-740Q	200000	100000000		-		-	-	0.242	-	-	3.714%
2014-07-18T01:20:00	Jocelyn Larouche	Manual testing	262293	262293		-		-	-	0.011	-	-	0.807%
2014-10-18T13:18:00	Jocelyn Larouche	Manual testing	324586	324586		-		-	-	0.014	-	-	0.905%
2015-10-16T08:06:38	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.055	-	-	3.170%
2016-03-26T12:20:29	Jocelyn Larouche	Manual testing	1202295	1202295		-		-	-	0.052	-	-	1.680%
2016-05-17T17:05:54	Bruno Victal	4790K-windows	2500000	62500000	12	-		-	-	0.248	-	-	5.071%
2018-03-25T11:41:48	Jocelyn Larouche	low 4M	1222295	122229500	12	-		-	-	0.336	-	-	5.232%
2018-10-21T20:52:08	Jocelyn Larouche	low 4M	1222295	206069800	12	-		-	-	0.532	-	-	5.666%
2018-11-19T20:31:52	Jocelyn Larouche	Manual testing	1222295	207100149		-		-	-	0.535	-	-	5.670%
2022-01-31T16:09:58	mognuts	Strand	115000	3047384340		-		-	-	7.140	-	-	5.176%
2022-05-24T01:24:59	axn	Manual testing	28000000	85350951840		-		-	-	201.0	-	-	14.944%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.019	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.037	-	-
2016-02-23T16:28:19	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.112	-	-
2009-02-14T15:16:00	Sturle Sunde	danzi.ifi	2⁶⁰	2⁶¹		-	-	0.149	-	-
2010-11-08T09:10:00	Michael C	Manual testing	2⁶¹	2⁶²		-	-	0.298	-	-
2010-11-29T00:12:00	Michael C	Manual testing	2⁶²	2⁶³		-	-	0.953	-	-
2010-11-29T00:12:00	Michael C	Manual testing	2⁶³	2⁶⁴		-	-	1.905	-	-
2013-03-22T15:19:00	Never Odd Or Even	Manual testing	2⁶⁴	2⁶⁵		-	-	3.626	-	-
2013-03-22T15:19:00	Never Odd Or Even	Manual testing	2⁶⁵	2⁶⁶		-	-	7.253	-	-
2013-03-22T15:19:00	Never Odd Or Even	Manual testing	2⁶⁶	2⁶⁷		-	-	14.51	-	-
2013-03-22T15:19:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	29.01	-	-
2013-05-02T11:26:00	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	58.02	-	-
2013-05-02T11:26:00	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰		-	-	116.0	-	-
2014-04-01T16:42:00	Never Odd Or Even	Manual testing	2⁷⁰	2⁷¹		-	-	232.1	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.483 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.483 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	9.81
250000	25000000		44	7.677

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-21T19:07:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-02-18T18:19:00	Steve Scott	Printer-2	50000	5000000						3	0.105
2008-11-29T05:59:00	J.Kampmeier	Big_Brother_2	50000	5000000						3	0.105
2009-03-20T05:45:00	Sturle Sunde	v23	50000	5000000						3	0.105
2009-07-29T23:04:00	maxybo	CB418E216	50000	5000000						3	0.105
2009-10-20T06:29:00	SubPrime	c2d0	50000	5000000						3	0.105
2010-02-26T03:29:00	arnaud	SRV-150	50000	5000000						3	0.105
2010-10-01T09:10:00	Ken Warner	red	50000	5000000						3	0.105
2011-02-03T14:46:00	Eric Christenson	ca_robotics_6	50000	5000000						3	0.105
2011-11-09T13:10:00	Pool Party	sts	50000	5000000						3	0.105
2012-06-19T00:32:00	schelle	ibm	50000	5000000						3	0.105
2012-10-27T10:32:00	Pool Party	sts	50000	5000000						3	0.105
2013-04-08T20:25:00	Pool Party	sts	50000	5000000						3	0.105
2013-08-10T08:17:00	Pool Party	sts	50000	5000000						3	0.105
2013-10-20T08:43:00	561	561	50000	5000000						3	0.105
2014-03-14T14:27:00	Bruce	snowflake	50000	5000000						3	0.105
2014-09-22T13:47:00	OS1	Tina	50000	5000000						3	0.105
2015-03-06T16:00:00	Bruce	desk16	50000	5000000						3	0.105
2015-05-10T22:34:00	arnaud	CHAMOT06	50000	5000000						3	0.105
2015-08-06T04:15:00	_^MvIiIaX^_	MDD-M540-1860M	50000	5000000						3	0.105
2015-10-26T23:26:51	Jason U	Dell-Win7	50000	5000000						3	0.105
2016-02-01T07:14:47	OS1	Tina	50000	5000000						3	0.105
2016-04-08T09:27:48	raman22feb1988	Suganya	50000	5000000						3	0.105
2016-05-19T09:28:33	Jason U	Dell-Win7	50000	5000000						3	0.105
2016-05-21T16:49:41	raman22feb1988	Santhosh	50000	5000000						3	0.105
2016-08-27T20:55:47	Bruno Victal	5820K-factoring	50000	5000000						150	5.234
2017-09-22T15:56:14	TJAOI	Manual testing	50000	5000000						58	2.024
2020-02-17T11:28:13	TJAOI	Manual testing	250000	25000000						44	7.677

date	userid	compid	res64	spent (GHz-days)
2002-02-03T00:00:00	ANONYMOUS	v4_computers	39162DAF696DF1C6	0.031
2016-06-01T18:46:57	MadPoo	Manual testing	39162DAF696DF1C6	0.031

date	userid	compid	cofactors	res64	PRP
2020-11-01T05:29:33	Ethan O'Connor	Manual testing		538A1ACA95D03635	no

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 = 28000000, B2 = 85350951840 (P-1 stage 2)

B1 = 115000, B2 = 3047384340 (P-1 stage 2)

B1 = 28000000 (P-1 stage 1)

B1 = 1222295, B2 = 207100149 (P-1 stage 2)

B1 = 1222295, B2 = 206069800 (P-1 stage 2)

B1 = 1222295, B2 = 122229500 (P-1 stage 2)

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

B1 = 200000, B2 = 100000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1222295 (P-1 stage 1)

B1 = 1202295 (P-1 stage 1)

B1 = 200000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 324586 (P-1 stage 1)

B1 = 262293 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 10000, B2 = 117500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 11000 (P-1 stage 1)

B1 = 10000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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