M736 027 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	80.9819	70.5882%	7500000	1103176824750	1,740.8039	19.0162%	1,821.7858	76.1812%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5947%	0.0010	62.0885%
Difference	+24	+80.9819	+16.0428%	+7488000	+1103176374750	+1,740.8028	+2.4215%	+1,821.7848	+14.0927%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
736027	15328571120532803420772286267649	32	103.596	10413049467297261799344512 2⁷ × 7 × 13 × 2087 × 3037 × 141045530477051	2022-10-03	3037	141045530477051	2.215e+11	222,542	415,647

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%
2002-02-03	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.351%
2002-03-24	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.650%
2002-05-11	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.077%
2002-07-14	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.642%
2002-11-24	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.345%
2003-06-23	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.174%
2011-07-10	Jocelyn Larouche	Manual testing	296597	296597		-		-	-	0.009	-	-	1.202%
2011-08-24	Jocelyn Larouche	Manual testing	494328	494328		-		-	-	0.014	-	-	1.535%
2011-10-15	Jocelyn Larouche	Manual testing	988656	988656		-		-	-	0.029	-	-	2.067%
2012-03-29	Jocelyn Larouche	Manual testing	1482985	1482985		-		-	-	0.043	-	-	2.420%
2013-10-29	David Campeau	i5-2500k	1485000	49005000		-		-	-	0.118	-	-	5.797%
2015-11-23	Sid & Andy	Bullseye	7360270	220808100	12	-		-	-	0.550	-	-	8.420%
2022-04-16	lycorn	supernova	7500000	1103176824750		-		-	-	1,741	-	-	19.016%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-05-31	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.007	-	-
2001-03-25	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.013	-	-
2001-12-01	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.026	-	-
2003-09-29	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.052	-	-
2008-10-11	Sturle Sunde	morovan.ifi	2⁵⁸	2⁵⁹		-	-	0.052	-	-
2008-10-11	Sturle Sunde	morovan.ifi	2⁵⁹	2⁶⁰		-	-	0.104	-	-
2010-06-18	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.209	-	-
2015-03-03	NR	Manual testing	2⁶¹	2⁶²		-	-	0.417	-	-
2015-10-17	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.334	-	-
2015-10-17	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.667	-	-
2016-04-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	5.076	-	-
2017-09-08	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	10.15	-	-
2020-05-10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	20.31	-	-
2022-03-23	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	40.61	-	-

ECM factoring results:

Total ECM effort:	16.622 GHz-days
Estimated T-Level:	25.877

Digits	B1	Complete	FacMiss
20	11000	17.190	0.000%
25	50000	2.008	13.429%
30	250000	0.175	83.916%
35	1000000	0.013	98.755%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	6.344
250000	25000000		61	6.911
250000	254268105		0	0.00000e+0
250000	254268105	15328571120532803420772286267649	7	3.367

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-30	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-01	Steve Scott	Abit	50000	5000000						1	0.023
2008-01-01	Steve Scott	Abit	50000	5000000						1	0.023
2008-07-16	Sturle Sunde	v21	50000	5000000						3	0.068
2008-11-14	Sturle Sunde	v21	50000	5000000						3	0.068
2009-02-14	Sturle Sunde	v21	50000	5000000						3	0.068
2009-04-11	mdrg	MDRG02	50000	5000000						3	0.068
2009-07-26	JimBa	atlserv	50000	5000000						3	0.068
2009-09-24	maxybo	CB418E216	50000	5000000						3	0.068
2009-11-24	fww	mercury	50000	5000000						3	0.068
2010-02-28	Lupo	yorick	50000	5000000						3	0.068
2010-06-26	maxybo	CB418E216	50000	5000000						3	0.068
2010-12-23	arnaud	Arnaud-PC	50000	5000000						3	0.068
2011-01-30	Jocelyn Larouche	Manual testing	50000	5000000						1	0.023
2011-04-08	Jocelyn Larouche	Manual testing	50000	5000000						1	0.023
2011-09-21	OS1	Tina	50000	5000000						3	0.068
2011-12-15	Pool Party	sts	50000	5000000						3	0.068
2012-06-17	alpertron	core2quad	50000	5000000						3	0.068
2012-08-29	alpertron	core2quad	50000	5000000						3	0.068
2013-01-06	gucs	echo3	50000	5000000						3	0.068
2013-03-16	gucs	echo3	50000	5000000						3	0.068
2013-05-17	gucs	echo3	50000	5000000						3	0.068
2013-07-18	gucs	echo3	50000	5000000						3	0.068
2013-09-20	gucs	echo3	50000	5000000						3	0.068
2013-11-22	gucs	echo3	50000	5000000						3	0.068
2014-01-24	gucs	echo3	50000	5000000						3	0.068
2014-02-28	Ryan Schulz	wenn	50000	5000000						15	0.340
2015-02-21	Bruce	desk16	50000	5000000						3	0.068
2015-02-24	Bruce	desk16	50000	5000000						3	0.068
2015-03-01	Bruce	desk16	50000	5000000						3	0.068
2015-07-20	mikr	MSI	50000	5000000						58	1.314
2016-06-03	TJAOI	Manual testing	50000	5000000						40	0.906
2016-08-31	westicles	Manual testing	50000	5000000						90	2.039
2017-12-15	Oussama Kiamouche	Home	250000	25000000						3	0.340
2018-12-24	Vitalii		250000	25000000						3	0.340
2019-01-25	TJAOI	Manual testing	250000	25000000						41	4.645
2021-11-10	mnd9	75203	250000	25000000						7	0.793
2022-01-15	Corey	tab	250000	25000000						7	0.793
2022-10-03	Luminescence	Monstrum	250000	254268105	15328571120532803420772286267649	103.596	7	2	7571763686613879	7	3.367
2022-10-03	Luminescence	Monstrum	250000	254268105						0	-

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Roger Gariépy		65464D28E237FF97	0.015
2015-04-11	MadPoo	Manual testing	65464D28E237FF97	0.015

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 = 7500000, B2 = 1103176824750 (P-1 stage 2)

B1 = 7360270, B2 = 220808100 (P-1 stage 2)

B1 = 7500000 (P-1 stage 1)

B1 = 7360270 (P-1 stage 1)

B1 = 1485000, B2 = 49005000 (P-1 stage 2)

B1 = 1485000 (P-1 stage 1)

B1 = 1482985 (P-1 stage 1)

B1 = 988656 (P-1 stage 1)

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

B1 = 494328 (P-1 stage 1)

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

B1 = 296597 (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

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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