M26 711 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	1,112.4225	77.6119%	5000000000	1516930270635780	54,262.8568	32.9667%	55,375.2793	84.9925%
Target	2⁴⁴	0.0001	65.9091%	500	50000	0.0000	1.6994%	0.0001	66.4884%
Difference	+23	+1,112.4224	+11.7028%	+4999999500	+1516930270585780	+54,262.8568	+31.2672%	+55,375.2792	+18.5041%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
26711	621751313066553887083597066693206407839	39	128.870	11638488133475981563468179152656329 3 × 7 × 47 × 59403527 × 198503049999863163717821	2016-09-01	59403527	198503049999863163717821	5.778e+12	7.100e+12	1.326e+13
26711	22174779495477897951746934409949580744225508700035 1471	54	177.211	4150870333472707489750839431310991865565779772385 5 × 1223 × 34591 × 41443 × 293899 × 1223723 × 1586912689 × 829648511816591	2023-04-11	1586912689	829648511816591	6.692e+12	29,677	55,427

exponent	prime factors	composite factor	digits	bits*
26711	621751313066553887083597066693206407839 22174779495477897951746934409949580744225508700035 1471	13787198268274678384624366664779740792133522949803 6705793616392346108392225422154942369581169	93	306.081

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	-	-	1.915%
2001-08-18	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.004	-	-	4.690%
2002-04-28	ANONYMOUS	v4_computers	16384	1638400		-		-	-	6.87752e-5	-	-	0.636%
2002-06-09	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.000	-	-	1.027%
2002-07-20	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.000	-	-	1.540%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.001	-	-	2.178%
2003-03-27	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.001	-	-	2.934%
2003-04-03	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.002	-	-	3.797%
2003-04-27	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.004	-	-	4.759%
2003-05-19	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.009	-	-	5.813%
2003-07-13	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.018	-	-	6.952%
2003-09-29	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.035	-	-	8.169%
2003-10-08	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.070	-	-	9.450%
2013-10-25	David Campeau	i5-2500k	304635000	304635000		-		-	-	0.200	-	-	7.846%
2013-11-03	David Campeau	i5-2500k	456950000	456950000		-		-	-	0.300	-	-	8.473%
2013-11-05	David Campeau	i5-2500k	456950000	10250490000		-		-	-	0.650	-	-	13.609%
2013-11-15	David Campeau	i5-2500k	609265000	609265000		-		-	-	0.400	-	-	8.926%
2013-11-18	David Campeau	i5-2500k	761580000	761580000		-		-	-	0.500	-	-	9.282%
2016-12-15	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-		-	-	0.668	-	-	13.595%
2023-02-07	nordi	sweet16_30.9b3	5000000000	5000000000		-		-	-	3.283	-	-	12.408%
2023-04-10	nordi	sweet16_30.8b14	5000000000	1516930270635780			22174779495477897951746934409949580744225508700035 1471	54	177.211	54,263	2.41883e-5	108,526	32.967%

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		-	-	0.022	-	-
2000-03-08	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.045	-	-
2000-10-07	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.359	-	-
2002-11-24	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.719	-	-
2016-02-23	LaurV	Manual testing	2⁵⁷	2⁵⁸		-	-	0.719	-	-
2009-01-18	Sturle Sunde	gnom.ifi	2⁵⁸	2⁵⁹		-	-	1.438	-	-
2009-01-31	Sturle Sunde	krebs.ifi	2⁵⁹	2⁶⁰		-	-	2.875	-	-
2012-04-02	bcp19	Manual testing	2⁶⁰	2⁶¹		-	-	5.750	-	-
2012-04-02	bcp19	Manual testing	2⁶¹	2⁶²		-	-	11.50	-	-
2016-09-14	Sid & Andy	Mrs_Potato_Head	2⁶²	2⁶³		-	-	36.75	-	-

ECM factoring results:

Total ECM effort:	339.712 GHz-days
Estimated T-Level:	41.153

Digits	B1	Complete	FacMiss
20	11000	1,794.133	0.000%
25	50000	468.068	0.000%
30	250000	93.856	0.000%
35	1000000	15.071	0.000%
40	3000000	1.999	13.542%
45	11000000	0.231	79.403%
50	44000000	0.023	97.707%
55	110000000	0.002	99.792%

ECM Summary

B1	B2	factor	curves	GHz-days
1000000	100000000		494	4.667
3000000	300000000		8,309	235.5
11000000	30114149530	621751313066553887083597066693206407839	100	99.6

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-04-05	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-04-05	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-04-06	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-04-06	Sturle Sunde	x	1000000	100000000						3	0.028
2009-04-06	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-04-07	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-04-07	Sturle Sunde	v17	1000000	100000000						3	0.028
2009-04-07	Sturle Sunde	x	1000000	100000000						3	0.028
2009-04-08	Sturle Sunde	v17	1000000	100000000						3	0.028
2009-04-09	Sturle Sunde	v17	1000000	100000000						3	0.028
2009-04-09	Sturle Sunde	x	1000000	100000000						3	0.028
2009-04-10	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-04-10	Carsten Kossendey	durandal	1000000	100000000						1	0.009
2009-04-11	Sturle Sunde	v22	1000000	100000000						3	0.028
2009-05-08	unconnected	saudi-E5405	1000000	100000000						100	0.945
2009-06-28	James Hintz	18_060209	1000000	100000000						100	0.945
2009-07-01	James Hintz	christine	1000000	100000000						150	1.417
2009-08-27	James Hintz	NEW_OMFG	3000000	300000000						100	2.834
2009-09-27	GrunwalderGIMP	GWPrime02	1000000	100000000						100	0.945
2009-11-24	Carsten Kossendey	Manual testing	1000000	100000000						1	0.009
2010-03-24	James Hintz	OMFG	3000000	300000000						10	0.283
2010-04-04	James Hintz	NEW_OMFG	3000000	300000000						60	1.701
2010-04-07	James Hintz	OMFG	3000000	300000000						11	0.312
2010-05-11	James Hintz	OMFG	3000000	300000000						11	0.312
2010-06-06	James Hintz	17_051310	3000000	300000000						11	0.312
2011-01-21	James Hintz	home2	3000000	300000000						11	0.312
2011-04-15	James Hintz	17_051310	3000000	300000000						11	0.312
2012-05-07	Anton Repko	triton	3000000	300000000						4042	114.6
2012-05-07	Anton Repko	triton	3000000	300000000						4042	114.6
2016-09-01	Anton Repko	Manual testing	11000000	30114149530	621751313066553887083597066693206407839	128.870	100	2		100	99.6

date	userid	compid	res64	spent (GHz-days)
1997-01-01	George Woltman		889BCA6078D3C950	1.20941e-5
2015-04-11	MadPoo	Manual testing	889BCA6078D3C950	1.20941e-5

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

621751313066553887083597066693206407839

CA62C0F1263AEC__

2017-09-21

Oliver Kruse

Manual testing

621751313066553887083597066693206407839

CA62C0F1263AEC__

2017-10-12

kkmrkkblmbrbk

Manual testing

621751313066553887083597066693206407839

CA62C0F1263AEC__

2020-04-17

Oliver Kruse

Manual testing

621751313066553887083597066693206407839

F9F1F083D8F3E4__

2023-04-11

nordi

sweet16_30.9b3

621751313066553887083597066693206407839

22174779495477897951746934409949580744225508700035
1471

F9F1F083D8F3E4C4

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 = 5000000000, B2 = 1516930270635780 (P-1 stage 2)

B1 = 5000000000 (P-1 stage 1)

B1 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 456950000, B2 = 10250490000 (P-1 stage 2)

B1 = 761580000 (P-1 stage 1)

B1 = 609265000 (P-1 stage 1)

B1 = 500000000 (P-1 stage 1)

B1 = 456950000 (P-1 stage 1)

B1 = 304635000 (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)

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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