M725 723 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	82.1317	70.5882%	100000000	2002602952350	3,162.4563	22.9447%	3,244.5880	77.3367%
Target	2⁴⁴	0.0000	54.5455%	12000	2250000	0.0039	16.5681%	0.0039	62.0764%
Difference	+24	+82.1317	+16.0428%	+99988000	+2002600702350	+3,162.4524	+6.3766%	+3,244.5841	+15.2603%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
725723	59731274813394699981429528239391708732703	41	135.456	41152943212075888446025224665190237 3 × 13² × 23 × 12653 × 116507 × 335999 × 21982423 × 324120151	2022-12-03	21982423	324120151	2.423e+11	1.1133	1.2956

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	-	-	0.159%
2002-01-28	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.350%
2002-03-16	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.648%
2002-05-11	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.074%
2002-07-14	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.638%
2002-11-16	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.340%
2003-06-17	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.168%
2011-02-24	Jocelyn Larouche	Manual testing	400000	400000		-		-	-	0.012	-	-	1.388%
2011-08-20	Jocelyn Larouche	Manual testing	503447	503447		-		-	-	0.015	-	-	1.544%
2011-10-08	Jocelyn Larouche	Manual testing	1006895	1006895		-		-	-	0.029	-	-	2.078%
2012-03-20	Jocelyn Larouche	Manual testing	1510343	1510343		-		-	-	0.044	-	-	2.432%
2012-11-05	Jocelyn Larouche	Manual testing	2494484	2494484		-		-	-	0.072	-	-	2.914%
2015-04-08	Jocelyn Larouche	Manual testing	2743932	2743932		-		-	-	0.079	-	-	3.010%
2015-05-01	Jocelyn Larouche	Manual testing	3320157	3320157		-		-	-	0.096	-	-	3.209%
2015-05-22	Jocelyn Larouche	Manual testing	3652172	3652172		-		-	-	0.106	-	-	3.311%
2015-06-08	Jocelyn Larouche	Manual testing	4017389	4017389		-		-	-	0.116	-	-	3.414%
2015-06-25	Jocelyn Larouche	Manual testing	4419127	4419127		-		-	-	0.128	-	-	3.519%
2015-09-15	Jocelyn Larouche	Manual testing	4861039	4861039		-		-	-	0.141	-	-	3.626%
2015-09-18	Jocelyn Larouche	Manual testing	5347142	5347142		-		-	-	0.155	-	-	3.734%
2015-09-20	Jocelyn Larouche	Manual testing	5881856	5881856		-		-	-	0.170	-	-	3.844%
2015-09-27	Jocelyn Larouche	Manual testing	6470041	6470041		-		-	-	0.187	-	-	3.956%
2015-09-29	Jocelyn Larouche	Manual testing	7117045	7117045		-		-	-	0.206	-	-	4.069%
2015-10-09	Jocelyn Larouche	Manual testing	8343972	8343972		-		-	-	0.242	-	-	4.262%
2015-10-12	Jocelyn Larouche	Manual testing	8859195	8859195		-		-	-	0.257	-	-	4.335%
2015-10-16	Jocelyn Larouche	Manual testing	9374418	9374418		-		-	-	0.271	-	-	4.405%
2015-10-20	Jocelyn Larouche	Manual testing	9889641	9889641		-		-	-	0.286	-	-	4.472%
2015-10-28	Jocelyn Larouche	Manual testing	10404864	10404864		-		-	-	0.301	-	-	4.536%
2015-11-06	Jocelyn Larouche	Manual testing	10920087	10920087		-		-	-	0.316	-	-	4.597%
2015-11-11	Jocelyn Larouche	Manual testing	11435310	11435310		-		-	-	0.331	-	-	4.656%
2015-11-13	Jocelyn Larouche	Manual testing	11950533	11950533		-		-	-	0.346	-	-	4.712%
2015-11-18	Jocelyn Larouche	Manual testing	12465756	12465756		-		-	-	0.361	-	-	4.767%
2015-11-28	Sid & Andy	Bullseye	9889641	296689230	12	-		-	-	0.739	-	-	8.947%
2016-08-23	Jocelyn Larouche	Manual testing	13712331	593378460	12	-		-	-	1.312	-	-	10.049%
2022-11-15	Jocelyn Larouche	Manual testing	15337781	14789624850		-		-	-	23.76	-	-	14.443%
2022-12-03	lycorn	supernova	100000000	2002602952350			59731274813394699981429528239391708732703	41	135.456	3,162	0.029	6,325	22.945%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-12-23	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	-	-
2001-10-25	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.026	-	-
2003-09-21	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.053	-	-
2008-10-13	Sturle Sunde	klughardt.ifi	2⁵⁸	2⁵⁹		-	-	0.053	-	-
2008-10-13	Sturle Sunde	klughardt.ifi	2⁵⁹	2⁶⁰		-	-	0.106	-	-
2010-06-18	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.212	-	-
2015-03-02	NR	Manual testing	2⁶¹	2⁶²		-	-	0.423	-	-
2015-10-15	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.353	-	-
2015-10-15	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.705	-	-
2016-04-26	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	5.148	-	-
2017-08-07	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	10.30	-	-
2020-05-10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	20.59	-	-
2022-03-27	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	41.19	-	-

ECM factoring results:

Total ECM effort:	15.568 GHz-days
Estimated T-Level:	25.941

Digits	B1	Complete	FacMiss
20	11000	18.078	0.000%
25	50000	2.129	11.899%
30	250000	0.188	82.852%
35	1000000	0.014	98.653%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	280	6.336
250000	25000000	58	6.562
250000	27500000	7	0.820
250000	36500000	7	0.921
250000	37250000	7	0.929

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-29	Chad Davis	Bayes	50000	5000000						1	0.023
2007-12-30	James Heinrich	WHS	50000	5000000						1	0.023
2007-12-31	James Heinrich	WHS	50000	5000000						1	0.023
2008-06-29	Sturle Sunde	v1	50000	5000000						3	0.068
2008-11-11	Sturle Sunde	v23	50000	5000000						3	0.068
2009-04-11	Net_Force	Vista64	50000	5000000						3	0.068
2009-04-16	Sturle Sunde	v23	50000	5000000						3	0.068
2009-07-21	maxybo	CB418E216	50000	5000000						3	0.068
2009-10-17	fww	mercury	50000	5000000						3	0.068
2009-11-09	SubPrime	c2d0	50000	5000000						3	0.068
2010-06-10	Mustfindit	Ann	50000	5000000						3	0.068
2010-06-15	Charles A. Morris	pulsar	50000	5000000						3	0.068
2010-11-30	Boots	rchok28bo	50000	5000000						3	0.068
2011-01-30	Jocelyn Larouche	Manual testing	50000	5000000						1	0.023
2011-03-07	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.068
2012-02-01	Carsten Kossendey	durandal	50000	5000000						10	0.226
2012-12-20	Pool Party	sts	50000	5000000						3	0.068
2013-02-25	gucs	echo3	50000	5000000						3	0.068
2013-04-28	Sara	Sara	50000	5000000						3	0.068
2013-06-27	gucs	echo3	50000	5000000						3	0.068
2013-08-28	gucs	echo3	50000	5000000						3	0.068
2013-10-30	gucs	echo3	50000	5000000						3	0.068
2014-01-01	gucs	echo3	50000	5000000						3	0.068
2014-02-13	gucs	echo3	50000	5000000						3	0.068
2014-03-23	gucs	echo3	50000	5000000						3	0.068
2014-04-21	Ryan Schulz	wenn	50000	5000000						15	0.339
2015-02-27	Bruce	desk16	50000	5000000						3	0.068
2015-05-18	guru	h1	50000	5000000						3	0.068
2015-06-11	mikr	MSI	50000	5000000						58	1.312
2016-06-24	TJAOI	Manual testing	50000	5000000						37	0.837
2016-09-09	westicles	Manual testing	50000	5000000						90	2.037
2017-11-28	jafarism	jafarism-r06-26	250000	25000000						3	0.339
2018-11-30	TJAOI	Manual testing	250000	25000000						41	4.639
2021-07-19	monsted	rootweiler	250000	25000000						7	0.792
2021-10-01	mnd9	75202	250000	25000000						7	0.792
2021-12-02	Luminescence	Main	250000	36500000						7	0.921
2022-03-08	Brian Schroeder	i5-6600k	250000	27500000						7	0.820
2022-06-23	Oliver Kruse	Krusen-NAS	250000	37250000						7	0.929

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Ken Kriesel		E5D00A60E295FC94	0.014
2002-10-07	ANONYMOUS	v4_computers	E5D00A60E295FC94	0.014
2015-04-11	MadPoo	Manual testing	E5D00A60E295FC94	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 = 100000000, B2 = 2002602952350 (P-1 stage 2)

B1 = 15337781, B2 = 14789624850 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

B1 = 13712331, B2 = 593378460 (P-1 stage 2)

B1 = 9889641, B2 = 296689230 (P-1 stage 2)

B1 = 15337781 (P-1 stage 1)

B1 = 13712331 (P-1 stage 1)

B1 = 12465756 (P-1 stage 1)

B1 = 11950533 (P-1 stage 1)

B1 = 11435310 (P-1 stage 1)

B1 = 10920087 (P-1 stage 1)

B1 = 10404864 (P-1 stage 1)

B1 = 9889641 (P-1 stage 1)

B1 = 9374418 (P-1 stage 1)

B1 = 8859195 (P-1 stage 1)

B1 = 8343972 (P-1 stage 1)

B1 = 7117045 (P-1 stage 1)

B1 = 6470041 (P-1 stage 1)

B1 = 5881856 (P-1 stage 1)

B1 = 5347142 (P-1 stage 1)

B1 = 4861039 (P-1 stage 1)

B1 = 4419127 (P-1 stage 1)

B1 = 4017389 (P-1 stage 1)

B1 = 3652172 (P-1 stage 1)

B1 = 3320157 (P-1 stage 1)

B1 = 2743932 (P-1 stage 1)

B1 = 2494484 (P-1 stage 1)

B1 = 1510343 (P-1 stage 1)

B1 = 1006895 (P-1 stage 1)

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

B1 = 503447 (P-1 stage 1)

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

B1 = 400000 (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 = 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

10¹¹

10¹²

10¹³

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