M720 221 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	82.7591	70.5882%	24000000	1200000000	2.5505	11.3241%	85.3097	73.9188%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5537%	0.0010	62.0699%
Difference	+24	+82.7591	+16.0428%	+23988000	+1199550000	+2.5495	-5.2297%	+85.3086	+11.8490%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
720221	48103801856595545044513538159408606417	38	125.177	33395167494835297113326005600648 2³ × 1049 × 2027 × 11443 × 56333 × 1903073 × 1600317581	2023-01-27	1903073	1600317581	2.124e+11	2.5771	4.7160

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-02	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.158%
2002-01-28	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.349%
2002-03-16	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.646%
2002-05-11	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.072%
2002-07-14	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.636%
2002-11-09	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.337%
2003-06-17	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.164%
2008-11-29	Jayson King	atlas	5000000	100000000		-		-	-	0.295	-	-	7.223%
2016-05-24	mikr	S058	24000000	1200000000	12	-		-	-	2.551	-	-	11.324%
2023-01-27	Jocelyn Larouche	Manual testing	1000000	4929814890			48103801856595545044513538159408606417	38	125.177	7.806	0.029	15.61	10.110%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-12-15	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2000-05-24	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.007	-	-
2000-05-31	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.007	-	-
2001-04-01	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.013	-	-
2001-10-20	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.027	-	-
2003-09-21	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.053	-	-
2008-10-11	Sturle Sunde	kinner.ifi	2⁵⁸	2⁵⁹		-	-	0.053	-	-
2008-10-11	Sturle Sunde	kinner.ifi	2⁵⁹	2⁶⁰		-	-	0.107	-	-
2010-06-17	Architects Cubed	a3_ss	2⁶⁰	2⁶¹		-	-	0.213	-	-
2015-03-01	NR	Manual testing	2⁶¹	2⁶²		-	-	0.427	-	-
2015-10-14	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.363	-	-
2015-10-14	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.726	-	-
2016-04-26	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	5.188	-	-
2017-07-20	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	10.38	-	-
2020-05-08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	20.75	-	-
2022-03-26	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	41.50	-	-

ECM factoring results:

Total ECM effort:	17.323 GHz-days
Estimated T-Level:	26.066

Digits	B1	Complete	FacMiss
20	11000	19.560	0.000%
25	50000	2.358	9.464%
30	250000	0.213	80.797%
35	1000000	0.016	98.444%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	280	6.332
250000	25000000	89	10.06
250000	37250000	7	0.928

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-29	Team_Bundu	bundu1	50000	5000000						1	0.023
2007-12-29	Steve Scott	Abit	50000	5000000						1	0.023
2007-12-29	Steve Scott	Abit	50000	5000000						1	0.023
2008-06-21	Sturle Sunde	v21	50000	5000000						3	0.068
2008-11-08	Sturle Sunde	v23	50000	5000000						3	0.068
2009-02-06	Sturle Sunde	v23	50000	5000000						3	0.068
2009-04-15	Smurgs	Praca	50000	5000000						3	0.068
2009-07-18	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.068
2009-09-15	ANONYMOUS	mpow	50000	5000000						3	0.068
2009-11-04	Geoff Wing	GW1	50000	5000000						3	0.068
2010-02-07	Geoff Wing	GW1	50000	5000000						3	0.068
2010-06-13	Charles A. Morris	pulsar	50000	5000000						3	0.068
2010-11-19	Donna Noble	PH2-955	50000	5000000						3	0.068
2011-01-27	arnaud	Arnaud-PC	50000	5000000						3	0.068
2011-10-02	Lukasz Wrobel	4_core_L	50000	5000000						3	0.068
2011-12-18	alpertron	core2quad	50000	5000000						3	0.068
2012-06-11	Pool Party	sts	50000	5000000						3	0.068
2012-08-27	OS1	Tina	50000	5000000						3	0.068
2013-01-02	gucs	echo3	50000	5000000						3	0.068
2013-03-11	gucs	echo3	50000	5000000						3	0.068
2013-05-06	Sara	Sara	50000	5000000						3	0.068
2013-07-09	gucs	echo3	50000	5000000						3	0.068
2013-09-16	alpertron	core2quad	50000	5000000						3	0.068
2013-11-09	gucs	echo3	50000	5000000						3	0.068
2014-01-12	gucs	echo3	50000	5000000						3	0.068
2014-02-19	Ryan Schulz	wenn	50000	5000000						15	0.339
2015-02-21	Bruce	desk16	50000	5000000						3	0.068
2015-02-23	Bruce	desk16	50000	5000000						3	0.068
2015-02-28	Bruce	desk16	50000	5000000						3	0.068
2015-05-24	mikr	MSI	50000	5000000						57	1.289
2016-06-10	TJAOI	Manual testing	50000	5000000						40	0.905
2016-09-11	westicles	Manual testing	50000	5000000						90	2.035
2017-06-19	Oussama Kiamouche	Home	250000	25000000						3	0.339
2018-06-20	Oussama Kiamouche	Home	250000	25000000						3	0.339
2018-10-19	TJAOI	Manual testing	250000	25000000						41	4.636
2021-09-09	-Anonymous-		250000	25000000						7	0.791
2021-10-20	TSRPrime	TSRLoftus	250000	25000000						7	0.791
2021-11-07	Oliver Kruse	Krusen-NAS	250000	37250000						7	0.928
2022-01-11	arnaud	ATTAX04	250000	25000000						7	0.791
2022-10-07	bernardo_s	jaguar	250000	25000000						7	0.791
2022-11-10	arnaud	ATTAX04	250000	25000000						7	0.791
2022-12-25	arnaud	ATTAX04	250000	25000000						7	0.791

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Ken Kriesel		2CED30144D30186E	0.014
2002-10-07	ANONYMOUS	v4_computers	2CED30144D30186E	0.014
2015-04-11	MadPoo	Manual testing	2CED30144D30186E	0.014

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 = 1000000, B2 = 4929814890 (P-1 stage 2)

B1 = 24000000, B2 = 1200000000 (P-1 stage 2)

B1 = 24000000 (P-1 stage 1)

B1 = 5000000, B2 = 100000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

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

B1 = 65537, B2 = 6553700 (P-1 stage 2)

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

B1 = 131072 (P-1 stage 1)

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

B1 = 65537 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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