M28 807 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	1,031.4825	77.6119%	8000000000	2253172624873170	98,054.7260	34.0376%	99,086.2085	85.2323%
Target	2⁴⁴	0.0001	65.9091%	500	50000	0.0000	1.7377%	0.0001	66.5015%
Difference	+23	+1,031.4825	+11.7028%	+7999999500	+2253172624823170	+98,054.7260	+32.2998%	+99,086.2084	+18.7308%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28807	6857518945523406873133566668158750818324839	43	142.299	119025218619144771637684706289421856117 7 × 211 × 227 × 619 × 43579469 × 1438212757 × 9150333341249	2023-07-27	1438212757	9150333341249	6.519e+12	399.27	743.70

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		-		-	-	0.001	-	-	1.938%
2001-08-18	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.005	-	-	4.731%
2002-04-28	ANONYMOUS	v4_computers	16384	1638400		-		-	-	8.36694e-5	-	-	0.646%
2002-06-09	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.000	-	-	1.041%
2002-07-20	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.000	-	-	1.560%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.001	-	-	2.204%
2003-03-27	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.001	-	-	2.965%
2003-04-03	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.003	-	-	3.833%
2003-04-27	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.005	-	-	4.801%
2003-05-19	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.011	-	-	5.860%
2003-07-13	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.021	-	-	7.004%
2003-09-29	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.043	-	-	8.227%
2003-10-08	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.086	-	-	9.512%
2013-11-07	David Campeau	i5-2500k	204545000	10636340000		-		-	-	0.617	-	-	13.438%
2017-05-30	mikr	S058	12000000000	960000000000	12	-		-	-	50.84	-	-	22.228%
2023-07-27	masser	Manual testing	8000000000	2253172624873170			6857518945523406873133566668158750818324839	43	142.299	98,055	3.17357e-5	196,109	34.038%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-05-07	ATH	5960X	500000000	101500000000	2	7			-	-	4.914
2023-07-07	masser	Manual testing	250000000	10000000000	91	37			-	-	0.719

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-10-21	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.021	-	-
2000-03-15	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.042	-	-
2000-10-15	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.333	-	-
2002-12-02	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.666	-	-
2016-02-23	LaurV	Manual testing	2⁵⁷	2⁵⁸		-	-	0.666	-	-
2009-01-14	Sturle Sunde	hoffman.ifi	2⁵⁸	2⁵⁹		-	-	1.333	-	-
2009-02-07	Sturle Sunde	zumthor.ifi	2⁵⁹	2⁶⁰		-	-	2.666	-	-
2012-04-02	bcp19	Manual testing	2⁶⁰	2⁶¹		-	-	5.332	-	-
2012-04-02	bcp19	Manual testing	2⁶¹	2⁶²		-	-	10.66	-	-
2016-09-20	Sid & Andy	Mrs_Potato_Head	2⁶²	2⁶³		-	-	34.08	-	-
2018-04-09	Yxinity	Elena	2⁶³	2⁶⁴		-	-	68.15	-	-
2018-04-10	Yxinity	Manual testing	2⁶³	2⁶⁴		-	-	68.15	-	-
2019-07-20	Yxinity	YGSMainFrame	2⁶⁴	2⁶⁵		-	-	129.7	-	-
2019-07-21	Yxinity	Manual testing	2⁶⁴	2⁶⁵		-	-	129.7	-	-
2020-05-24	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	259.4	-	-
2020-05-24	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	259.4	-	-

ECM factoring results:

Total ECM effort:	3,118.785 GHz-days
Estimated T-Level:	42.292

Digits	B1	Complete	FacMiss
20	11000	1,542.567	0.000%
25	50000	434.339	0.000%
30	250000	99.860	0.000%
35	1000000	18.992	0.000%
40	3000000	3.107	4.473%
45	11000000	0.458	63.232%
50	44000000	0.062	93.991%
55	110000000	0.008	99.222%

ECM Summary

B1	B2	curves	GHz-days
1000000	100000000	226	2.597
3000000	300000000	3,057	105.4
3000000	400000000	2,000	76.44
11000000	1100000000	110	13.91
11000000	35133391030	728	1,018
43000000	240490660426	204	1,902

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-05	Sturle Sunde	v17	1000000	100000000						3	0.034
2009-04-07	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-07	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-08	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-08	Sturle Sunde	v22	1000000	100000000						3	0.034
2009-04-09	Sturle Sunde	v22	1000000	100000000						3	0.034
2009-04-10	Sturle Sunde	x	1000000	100000000						3	0.034
2009-04-10	Carsten Kossendey	durandal	1000000	100000000						1	0.011
2009-04-11	Sturle Sunde	x	1000000	100000000						3	0.034
2009-05-06	unconnected	Q6600-turk	1000000	100000000						100	1.149
2009-06-05	unconnected	X3210-gr	3000000	300000000						100	3.448
2009-10-08	GrunwalderGIMP	GWPrime02	1000000	100000000						100	1.149
2009-11-24	Carsten Kossendey	Manual testing	1000000	100000000						1	0.011
2010-04-03	James Hintz	OMFG	3000000	300000000						10	0.345
2010-05-09	James Hintz	OMFG	3000000	300000000						11	0.379
2010-06-09	James Hintz	17_051310	3000000	300000000						11	0.379
2010-12-15	Oscar Östlin	Manual testing	3000000	300000000						1	0.034
2011-02-02	James Hintz	home2	3000000	300000000						11	0.379
2011-04-03	James Hintz	17_051310	3000000	300000000						11	0.379
2014-01-21	mikr	MSI	3000000	300000000						26	0.896
2014-02-04	mikr	MSI	3000000	300000000						41	1.414
2014-07-26	PageFault	Manual testing	3000000	300000000						150	5.172
2014-09-02	mikr	Dell	3000000	300000000						34	1.172
2015-08-28	lycorn	asteroid	3000000	300000000						250	8.620
2015-09-02	lycorn	asteroid	3000000	300000000						1400	48.27
2015-10-03	lycorn	asteroid	3000000	300000000						1000	34.48
2015-12-09	Alexander Dubrovin	Manual testing	3000000	300000000						1	0.034
2016-01-05	Gordon Spence	Manual testing	3000000	400000000						1000	38.22
2016-01-06	Gordon Spence	Manual testing	3000000	400000000						1000	38.22
2017-04-30	James Hintz	11_04_2016	11000000	1100000000						10	1.264
2017-06-08	James Hintz	11_04_2016	11000000	1100000000						100	12.64
2019-11-19	Ryan Propper	Manual testing	11000000	35133391030						728	1,018
2019-11-19	Ryan Propper	Manual testing	43000000	240490660426						204	1,902

date	userid	compid	res64	spent (GHz-days)
1997-01-01	George Woltman		DBBE6240726A93B4	1.58679e-5
2015-04-11	MadPoo	Manual testing	DBBE6240726A93B4	1.58679e-5

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 = 8000000000, B2 = 2253172624873170 (P-1 stage 2)

B1 = 12000000000, B2 = 960000000000 (P-1 stage 2)

B1 = 12000000000 (P-1 stage 1)

B1 = 8000000000 (P-1 stage 1)

B1 = 204545000, B2 = 10636340000 (P-1 stage 2)

B1 = 204545000 (P-1 stage 1)

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

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

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

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10³

10⁴

10⁵

10⁶

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10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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