M10 831 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	2,743.4140	79.1045%	1000000000000	1400243748567553890	14,503,593.3357	45.4482%	14,506,336.7498	88.6011%
Target	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.2951%	0.0002	68.5939%
Difference	+23	+2,743.4138	+10.9227%	+999999999500	+1400243748567543890	+14,503,593.3357	+44.1531%	+14,506,336.7495	+20.0072%

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	-	-	1.655%
2001-07-03	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.001	-	-	4.218%
2001-07-22	ANONYMOUS	v4_computers	43000000	4290000000		-		-	-	0.052	-	-	10.483%
2002-04-28	ANONYMOUS	v4_computers	16384	1638400		-		-	-	1.99153e-5	-	-	0.524%
2002-06-09	ANONYMOUS	v4_computers	32768	3276800		-		-	-	3.98305e-5	-	-	0.864%
2002-07-14	ANONYMOUS	v4_computers	65536	6553600		-		-	-	7.96610e-5	-	-	1.319%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.000	-	-	1.893%
2003-03-27	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.000	-	-	2.584%
2003-04-03	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.001	-	-	3.384%
2003-04-27	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.001	-	-	4.282%
2003-05-19	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.003	-	-	5.273%
2003-07-06	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.005	-	-	6.349%
2003-09-29	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.010	-	-	7.506%
2003-09-29	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.020	-	-	8.734%
2006-01-15	Jocelyn Larouche	v4_computers	110000000	110000000		-		-	-	0.021	-	-	5.835%
2006-01-15	Jocelyn Larouche	v4_computers	200000000	200000000		-		-	-	0.038	-	-	6.662%
2006-01-15	Jocelyn Larouche	v4_computers	300000000	300000000		-		-	-	0.057	-	-	7.247%
2012-12-20	bcp19	Toshiba-740Q	10000000000	100000000000		-		-	-	2.833	-	-	17.199%
2017-05-14	nordi	nordiputer	150022003227	7051034151676	12	-		-	-	100.0	-	-	25.177%
2022-02-21	-Anonymous-	T5810	100000000000	121047848166084840		-		-	-	1,253,805	-	-	40.407%
2022-06-19	-Anonymous-	T5810	1000000000000	1400243748567553890		-		-	-	14,503,593	-	-	45.448%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-05-12	ATH	5960X	1000000000	241000000000	2	7			-	-	2.725

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-09-14	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.055	-	-
1999-12-30	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.111	-	-
2000-06-28	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.443	-	-
2000-06-29	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.443	-	-
2000-08-17	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.886	-	-
2002-07-27	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	1.773	-	-
2016-02-23	LaurV	Manual testing	2⁵⁷	2⁵⁸		-	-	1.773	-	-
2010-07-20	George Woltman	Manual testing	2⁵⁸	2⁵⁹		-	-	3.545	-	-
2010-07-20	George Woltman	Manual testing	2⁵⁹	2⁶⁰		-	-	7.090	-	-
2012-11-08	bcp19	Manual testing	2⁶⁰	2⁶¹		-	-	14.18	-	-
2015-03-24	snme2pm1	G1	2⁶¹	2⁶²		-	-	28.36	-	-
2015-11-15	snme2pm1	G1	2⁶²	2⁶³		-	-	90.63	-	-
2018-09-12	snme2pm1	g10	2⁶³	2⁶⁴		-	-	181.3	-	-
2020-09-03	LaurV	Manual testing	2⁶⁴	2⁶⁵		-	-	345.0	-	-
2021-08-22	Ruslan Borisov	Manual testing	2⁶⁵	2⁶⁶		-	-	689.9	-	-

ECM factoring results:

Total ECM effort:	19,301.597 GHz-days
Estimated T-Level:	50.976

Digits	B1	Complete	FacMiss
20	11000	4,176.422	0.000%
25	50000	1,641.259	0.000%
30	250000	553.160	0.000%
35	1000000	146.854	0.000%
40	3000000	33.376	0.000%
45	11000000	6.702	0.123%
50	44000000	1.202	30.067%
55	110000000	0.195	82.269%
60	260000000	0.029	97.127%
65	800000000	0.004	99.598%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	280	0.038
830000	830000000	100	0.892
1000000	100000000	1,945	5.321
3000000	300000000	421	3.455
11000000	1100000000	294	8.847
43000000	240490660426	2,404	5,335
44000000	4400000000	4,575	550.7
110000000	11000000000	1	0.301
110000000	776278396540	1,884	13,397

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-02-20	David Campeau		1000000	100000000						100	0.274
2008-04-10	Matt	HP	1000000	100000000						10	0.027
2008-04-11	Matt	Matt	1000000	100000000						158	0.432
2008-04-12	Matt	Matt	1000000	100000000						97	0.265
2008-10-26	Jayson King	atlas	3000000	300000000						10	0.082
2008-11-09	Jayson King	atlas	11000000	1100000000						3	0.090
2008-11-11	Jayson King	atlas	3000000	300000000						5	0.041
2008-12-09	Jayson King	atlas	3000000	300000000						100	0.821
2009-01-23	klajok	Manual testing	3000000	300000000						100	0.821
2009-02-13	kiwiboy		3000000	300000000						6	0.049
2009-02-24	klajok	Manual testing	3000000	300000000						100	0.821
2009-04-19	eteo	stephanie	44000000	4400000000						100	12.04
2009-04-24	Carsten Kossendey	durandal	11000000	1100000000						1	0.030
2009-05-11	unconnected	Q6600-turk	3000000	300000000						100	0.821
2009-06-06	unconnected	saudi-E5405	44000000	4400000000						100	12.04
2009-09-25	James Hintz	01_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	08_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	04_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	07_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	05_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	12_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	06_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	11_091909	11000000	1100000000						3	0.090
2009-09-25	James Hintz	02_091909	11000000	1100000000						3	0.090
2009-09-26	James Hintz	10_091909	11000000	1100000000						3	0.090
2009-09-26	James Hintz	19_091909	11000000	1100000000						3	0.090
2009-09-26	James Hintz	09_091909	11000000	1100000000						3	0.090
2009-09-27	James Hintz	20_091909	11000000	1100000000						3	0.090
2009-09-28	James Hintz	17_091909	11000000	1100000000						3	0.090
2009-09-29	James Hintz	13_091909	11000000	1100000000						3	0.090
2009-09-29	James Hintz	15_091909	11000000	1100000000						3	0.090
2009-09-29	James Hintz	18_091909	11000000	1100000000						3	0.090
2009-09-29	James Hintz	16_091909	11000000	1100000000						3	0.090
2009-11-20	Carsten Kossendey	Manual testing	11000000	1100000000						10	0.301
2010-03-12	James Hintz	15_122109	11000000	1100000000						50	1.505
2010-03-13	James Hintz	15_122109	11000000	1100000000						50	1.505
2010-03-14	James Hintz	15_122109	11000000	1100000000						50	1.505
2010-03-18	Bud	annan	110000000	11000000000						1	0.301
2010-04-30	James Hintz	15_122109	11000000	1100000000						11	0.331
2010-05-08	James Hintz	15_122109	11000000	1100000000						11	0.331
2010-05-09	James Hintz	15_122109	11000000	1100000000						11	0.331
2010-05-09	James Hintz	15_122109	11000000	1100000000						11	0.331
2010-06-18	James Hintz	15_122109	11000000	1100000000						11	0.331
2010-06-19	James Hintz	15_122109	11000000	1100000000						11	0.331
2010-11-15	BloodIce	Mjolnir	11000000	1100000000						10	0.301
2012-11-02	Le Comte	S761	44000000	4400000000						1	0.120
2012-12-31	Sergiosi	Manual testing	44000000	4400000000						200	24.07
2015-04-22	mikr	MSI	44000000	4400000000						303	36.47
2015-12-07	ATH	xps	44000000	4400000000						1	0.120
2016-09-21	Adam Buran	yah	830000	830000000						100	0.892
2016-10-30	volki	Manual testing	44000000	4400000000						150	18.06
2016-11-27	volki	Manual testing	44000000	4400000000						150	18.06
2017-01-01	volki	Manual testing	44000000	4400000000						150	18.06
2017-01-04	Sid & Andy	Hand_In_The_Box	44000000	4400000000						100	12.04
2017-04-15	Sid & Andy	Etch	44000000	4400000000						100	12.04
2017-04-18	James Hintz	11_04_2016	44000000	4400000000						10	1.204
2017-05-21	James Hintz	11_04_2016	44000000	4400000000						100	12.04
2017-05-21	Sid & Andy	Etch	44000000	4400000000						100	12.04
2017-05-21	James Hintz	11_04_2016	44000000	4400000000						100	12.04
2017-05-26	James Hintz	11_04_2016	44000000	4400000000						100	12.04
2017-06-15	Ismo Laitela	6600K	44000000	4400000000						100	12.04
2017-06-20	Sid & Andy	Etch	44000000	4400000000						100	12.04
2017-06-27	James Hintz	alek_07_13_2016	44000000	4400000000						100	12.04
2017-06-27	James Hintz	alek_07_13_2016	44000000	4400000000						100	12.04
2017-06-27	James Hintz	alek_07_13_2016	44000000	4400000000						100	12.04
2017-06-27	James Hintz	alek_07_13_2016	44000000	4400000000						100	12.04
2017-07-12	Sid & Andy	Woody	44000000	4400000000						100	12.04
2017-07-29	Sid & Andy	Etch	44000000	4400000000						100	12.04
2017-07-31	Sid & Andy	Woody	44000000	4400000000						100	12.04
2017-08-05	Sid & Andy	Rocky	44000000	4400000000						100	12.04
2017-09-02	Sid & Andy	Rocky	44000000	4400000000						100	12.04
2017-09-15	Sid & Andy	Mr_Mike	44000000	4400000000						100	12.04
2017-12-29	James Hintz	10_12_2017	44000000	4400000000						100	12.04
2018-01-11	James Hintz	10_12_2017	44000000	4400000000						100	12.04
2018-02-03	James Hintz	10_12_2017	44000000	4400000000						100	12.04
2018-02-13	James Hintz	10_12_2017	44000000	4400000000						100	12.04
2018-02-25	James Hintz	10_12_2017	44000000	4400000000						100	12.04
2018-03-10	James Hintz	3_1_2018	44000000	4400000000						100	12.04
2018-04-18	James Hintz	3_1_2018	44000000	4400000000						100	12.04
2018-06-03	James Hintz	3_1_2018	44000000	4400000000						100	12.04
2018-07-28	James Hintz	3_1_2018	44000000	4400000000						100	12.04
2018-09-20	James Hintz	3_1_2018	44000000	4400000000						100	12.04
2018-10-31	James Hintz	3_1_2018	44000000	4400000000						100	12.04
2019-05-12	James Hintz	5_9_2018_work	44000000	4400000000						500	60.18
2019-09-02	_p95holder_	TFL16_PRPt11-E_b	50000	5000000						280	0.038
2019-10-01	Bigos2	Manual testing	44000000	4400000000						5	0.602
2019-11-19	Ryan Propper	Manual testing	43000000	240490660426						2404	5,335
2019-11-19	Ryan Propper	Manual testing	110000000	776278396540						1884	13,397
2019-12-11	Bigos2	Manual testing	44000000	4400000000						5	0.602
2021-04-24	_p95holder_	TFL16_PRPt11-E_b	1000000	100000000						1580	4.322

date	userid	compid	res64	spent (GHz-days)
1997-01-01	George Woltman		E659AD6EED5F45BA	1.42006e-6
2015-04-11	MadPoo	Manual testing	E659AD6EED5F45BA	1.42006e-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 = 1400243748567553890 (P-1 stage 2)

B1 = 100000000000, B2 = 121047848166084840 (P-1 stage 2)

B1 = 1000000000000 (P-1 stage 1)

B1 = 150022003227, B2 = 7051034151676 (P-1 stage 2)

B1 = 150022003227 (P-1 stage 1)

B1 = 100000000000 (P-1 stage 1)

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

B1 = 10000000000 (P-1 stage 1)

B1 = 300000000 (P-1 stage 1)

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

B1 = 200000000 (P-1 stage 1)

B1 = 110000000 (P-1 stage 1)

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 = 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

10¹²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

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