M14 723 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	2,018.1972	79.1045%	1000000000000	1401075893663576130	26,380,250.7062	45.8355%	26,382,268.9034	88.6820%
Target	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.4221%	0.0002	68.6343%
Difference	+23	+2,018.1971	+10.9227%	+999999999500	+1401075893663566130	+26,380,250.7062	+44.4134%	+26,382,268.9032	+20.0477%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-04-29	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.000	-	-	1.739%
2001-07-17	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.002	-	-	4.374%
2001-10-06	ANONYMOUS	v4_computers	43000000	4290000000		-		-	-	0.095	-	-	10.742%
2002-04-28	ANONYMOUS	v4_computers	16384	1638400		-		-	-	3.62019e-5	-	-	0.560%
2002-06-09	ANONYMOUS	v4_computers	32768	3276800		-		-	-	7.24038e-5	-	-	0.917%
2002-07-14	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.000	-	-	1.391%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.000	-	-	1.986%
2003-03-27	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.001	-	-	2.699%
2003-04-03	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.001	-	-	3.520%
2003-04-27	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.002	-	-	4.440%
2003-05-19	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.005	-	-	5.452%
2003-07-06	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.009	-	-	6.549%
2003-09-29	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.019	-	-	7.726%
2003-09-29	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.037	-	-	8.973%
2011-05-18	Jocelyn Larouche	Manual testing	400000000	400000000		-		-	-	0.138	-	-	7.871%
2012-10-12	Jocelyn Larouche	Manual testing	584608539	584608539		-		-	-	0.202	-	-	8.452%
2013-03-30	bcp19	Toshiba-740Q	10000000000	100000000000		-		-	-	5.150	-	-	17.484%
2018-06-20	James Hintz	3_1_2018	23515340287	1763650521525	12	-		-	-	40.89	-	-	22.748%
2022-03-25	-Anonymous-	T5810	100000000000	100013732677278420		-		-	-	1,883,125	-	-	40.537%
2023-04-12	-Anonymous-	T5810	1000000000000	1401075893663576130		-		-	-	26,380,251	-	-	45.836%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-05-11	ATH	5960X	1000000000	241000000000	2	7			-	-	4.954

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-09	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.041	-	-
1999-09-14	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.041	-	-
2000-03-01	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.081	-	-
2000-09-15	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.652	-	-
2002-08-31	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	1.304	-	-
2016-02-23	LaurV	Manual testing	2⁵⁷	2⁵⁸		-	-	1.304	-	-
2010-07-04	George Woltman	Manual testing	2⁵⁸	2⁵⁹		-	-	2.608	-	-
2010-07-04	George Woltman	Manual testing	2⁵⁹	2⁶⁰		-	-	5.216	-	-
2012-12-25	bcp19	Manual testing	2⁶⁰	2⁶¹		-	-	10.43	-	-
2015-08-03	snme2pm1	G1	2⁶¹	2⁶²		-	-	20.86	-	-
2016-07-19	Sid & Andy	Woody	2⁶²	2⁶³		-	-	66.67	-	-
2018-08-28	Anton Repko	Manual testing	2⁶³	2⁶⁴		-	-	133.3	-	-
2018-12-24	Anton Repko	Manual testing	2⁶⁴	2⁶⁵		-	-	253.8	-	-
2021-11-20	Ruslan Borisov	Manual testing	2⁶⁵	2⁶⁶		-	-	507.6	-	-

ECM factoring results:

Total ECM effort:	11,790.986 GHz-days
Estimated T-Level:	47.715

Digits	B1	Complete	FacMiss
20	11000	4,134.803	0.000%
25	50000	1,494.171	0.000%
30	250000	418.458	0.000%
35	1000000	98.000	0.000%
40	3000000	19.533	0.000%
45	11000000	3.444	3.194%
50	44000000	0.543	58.097%
55	110000000	0.078	92.509%
60	260000000	0.010	98.976%
65	800000000	0.001	99.887%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	280	0.070
1000000	100000000	2,153	10.71
3000000	300000000	111	1.656
11000000	1100000000	7,888	431.5
43000000	240490660426	2,748	11,086
44000000	4400000000	1,191	260.6

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-26	GrunwalderGIMP	GWPrime02	1000000	100000000						563	2.800
2009-02-15	Jayson King	atlas	1000000	100000000						10	0.050
2009-04-24	Carsten Kossendey	durandal	3000000	300000000						1	0.015
2009-05-08	unconnected	kuwait-X3220	44000000	4400000000						30	6.564
2009-05-15	unconnected	Q6600-turk	3000000	300000000						100	1.492
2009-05-27	unconnected	X3210-gr	44000000	4400000000						50	10.94
2009-08-02	eteo	sansan	11000000	1100000000						25	1.368
2009-09-28	James Hintz	08_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	01_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	04_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	03_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	05_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	07_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	12_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	02_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	11_091909	11000000	1100000000						3	0.164
2009-09-28	James Hintz	06_091909	11000000	1100000000						3	0.164
2009-09-29	James Hintz	10_091909	11000000	1100000000						3	0.164
2009-09-29	James Hintz	19_091909	11000000	1100000000						3	0.164
2009-09-29	James Hintz	09_091909	11000000	1100000000						3	0.164
2009-09-30	James Hintz	20_091909	11000000	1100000000						3	0.164
2009-10-02	James Hintz	17_091909	11000000	1100000000						3	0.164
2009-10-03	James Hintz	13_091909	11000000	1100000000						3	0.164
2009-10-03	James Hintz	18_091909	11000000	1100000000						3	0.164
2009-10-03	James Hintz	15_091909	11000000	1100000000						3	0.164
2009-10-03	James Hintz	16_091909	11000000	1100000000						3	0.164
2009-11-20	Carsten Kossendey	Manual testing	3000000	300000000						10	0.149
2010-03-25	Bud	annan	11000000	1100000000						10	0.547
2013-01-02	Sergiosi	Manual testing	11000000	1100000000						200	10.94
2014-08-19	Carsten Kossendey	mother	11000000	1100000000						183	10.01
2014-08-21	Carsten Kossendey	mother	11000000	1100000000						183	10.01
2014-08-24	Carsten Kossendey	mother	11000000	1100000000						183	10.01
2014-11-20	Andres Aitsen	S761	11000000	1100000000						6	0.328
2015-01-09	Carsten Kossendey	leela	11000000	1100000000						183	10.01
2015-01-12	Carsten Kossendey	leela	11000000	1100000000						183	10.01
2015-01-12	Carsten Kossendey	leela	11000000	1100000000						183	10.01
2015-01-12	Carsten Kossendey	leela	11000000	1100000000						183	10.01
2015-04-18	Carsten Kossendey	mother	11000000	1100000000						575	31.45
2015-04-20	Carsten Kossendey	mother	11000000	1100000000						575	31.45
2015-04-21	Carsten Kossendey	mother	11000000	1100000000						574	31.40
2015-05-03	Carsten Kossendey	mother	11000000	1100000000						574	31.40
2015-10-11	Carsten Kossendey	tycho	11000000	1100000000						600	32.82
2015-11-11	Carsten Kossendey	tycho	11000000	1100000000						900	49.23
2015-11-13	Carsten Kossendey	tycho	11000000	1100000000						900	49.23
2015-11-26	Carsten Kossendey	leela	11000000	1100000000						1611	88.12
2015-12-08	ATH	xps	44000000	4400000000						1	0.219
2017-01-20	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	21.88
2017-03-27	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	21.88
2017-04-23	James Hintz	11_04_2016	44000000	4400000000						10	2.188
2017-05-17	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	21.88
2017-07-03	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	21.88
2017-07-20	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	21.88
2017-07-24	Ismo Laitela	6600K	44000000	4400000000						100	21.88
2017-07-30	Sid & Andy	Mr_Mike	44000000	4400000000						100	21.88
2017-08-11	Sid & Andy	Bullseye	44000000	4400000000						100	21.88
2017-08-18	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	21.88
2017-08-29	Sid & Andy	Bullseye	44000000	4400000000						100	21.88
2017-09-27	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	21.88
2019-09-02	_p95holder_	TFL16_PRPt11-E_b	50000	5000000						280	0.070
2019-11-19	Ryan Propper	Manual testing	43000000	240490660426						2748	11,086
2021-05-18	_p95holder_	TFL16_PRPt11-E_b	1000000	100000000						1580	7.857

date	userid	compid	res64	spent (GHz-days)
1997-01-01	George Woltman		D3ECC51146EC2B52	3.50898e-6
2015-04-11	MadPoo	Manual testing	D3ECC51146EC2B52	3.50898e-6

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 = 1000000000000, B2 = 1401075893663576130 (P-1 stage 2)

B1 = 100000000000, B2 = 100013732677278420 (P-1 stage 2)

B1 = 1000000000000 (P-1 stage 1)

B1 = 23515340287, B2 = 1763650521525 (P-1 stage 2)

B1 = 100000000000 (P-1 stage 1)

B1 = 23515340287 (P-1 stage 1)

B1 = 10000000000, B2 = 100000000000 (P-1 stage 2)

B1 = 10000000000 (P-1 stage 1)

B1 = 584608539 (P-1 stage 1)

B1 = 400000000 (P-1 stage 1)

B1 = 43000000, B2 = 4290000000 (P-1 stage 2)

B1 = 16777216, B2 = 1677721600 (P-1 stage 2)

B1 = 8388608, B2 = 838860800 (P-1 stage 2)

B1 = 43000000 (P-1 stage 1)

B1 = 4194304, B2 = 419430400 (P-1 stage 2)

B1 = 16777216 (P-1 stage 1)

B1 = 2097152, B2 = 209715200 (P-1 stage 2)

B1 = 8388608 (P-1 stage 1)

B1 = 1048576, B2 = 104857600 (P-1 stage 2)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 4194304 (P-1 stage 1)

B1 = 524288, B2 = 52428800 (P-1 stage 2)

B1 = 2097152 (P-1 stage 1)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 1048576 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 524288 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10³

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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