M18 859 Mersenne number exponent details

is 2 ¹⁸⁸⁵⁹ - 1

has 5678 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	1,575.5829	77.6119%	5600000000	16709983434234090	388,328.3485	35.8055%	389,903.9314	85.6281%
Target	2⁴⁴	0.0001	65.9091%	500	50000	0.0000	1.5322%	0.0001	66.4314%
Difference	+23	+1,575.5828	+11.7028%	+5599999500	+16709983434184090	+388,328.3485	+34.2733%	+389,903.9313	+19.1967%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
18859	12927750951020348912074648363807	32	103.350	342747519778894663345740717 3 × 19 × 953 × 5281 × 1885859 × 633550412863	2008-04-24	1885859	633550412863	8.087e+12	14.724	27.499
18859	196480760599294802504182696233054482557605449	45	147.139	5209204109425070324624388786071755728236 2² × 7 × 233 × 251 × 883 × 3733 × 181397 × 174031447 × 30570826174939	2023-05-18	174031447	30570826174939	9.324e+12	710.51	1,326.9

exponent	prime factors	composite factor	digits	bits*
18859	12927750951020348912074648363807 196480760599294802504182696233054482557605449	25400543396947348827246001172011214276014423572969 01466685233755391717584343	76	250.489

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	-	-	1.811%
2001-07-29	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.003	-	-	4.503%
2001-08-18	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.003	-	-	4.503%
2002-04-28	ANONYMOUS	v4_computers	16384	1638400		-		-	-	4.46828e-5	-	-	0.590%
2002-06-09	ANONYMOUS	v4_computers	32768	3276800		-		-	-	8.93655e-5	-	-	0.961%
2002-07-14	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.000	-	-	1.451%
2003-02-02	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.000	-	-	2.064%
2003-03-27	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.001	-	-	2.795%
2003-04-03	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.001	-	-	3.633%
2003-04-27	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.003	-	-	4.570%
2003-05-19	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.006	-	-	5.599%
2003-07-06	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.011	-	-	6.714%
2003-09-29	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.023	-	-	7.908%
2003-09-29	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.046	-	-	9.169%
2023-05-18	JacobZ	GreatLakes	5600000000	16709983434234090			196480760599294802504182696233054482557605449	45	147.139	388,328	1.10954e-5	776,657	35.806%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-10-15	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.032	-	-
2000-03-08	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.064	-	-
2000-09-29	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.509	-	-
2002-10-19	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	1.018	-	-

ECM factoring results:

Total ECM effort:	18.136 GHz-days
Estimated T-Level:	36.039

Digits	B1	Complete	FacMiss
20	11000	303.388	0.000%
25	50000	68.337	0.000%
30	250000	12.061	0.001%
35	1000000	1.735	17.638%
40	3000000	0.208	81.232%
45	11000000	0.022	97.861%
50	44000000	0.002	99.803%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	97	0.030
250000	25000000	12	0.018
1000000	100000000	1,021	6.267
3000000	300000000	642	11.82

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-01	Rob_Dee	twopc	50000	5000000						19	0.006
2009-07-02	Rob_Dee	twopc	50000	5000000						19	0.006
2009-07-03	Rob_Dee	twopc	50000	5000000						19	0.006
2009-07-04	Rob_Dee	twopc	50000	5000000						19	0.006
2009-07-04	Rob_Dee	twopc	50000	5000000						21	0.006
2009-07-04	Rob_Dee	twopc	250000	25000000						12	0.018
2011-04-03	James Hintz	17_051310	1000000	100000000						11	0.068
2017-10-01	kkmrkkblmbrbk	r4.16xlarge-64	1000000	100000000						1010	6.199
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-22	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-01	Lin_yq		3000000	300000000						3	0.055
2019-11-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-11-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2020-06-23	James Hintz	work_lappy_5_16_2019	3000000	300000000						100	1.841
2022-02-21	nordi	sweet16_ccx2	3000000	300000000						500	9.207

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	George Woltman		02E02A509A2F6EE8	5.54769e-6

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

12927750951020348912074648363807

EC1D0297F318D3__

2017-09-21

Oliver Kruse

Manual testing

12927750951020348912074648363807

EC1D0297F318D3__

2017-10-12

kkmrkkblmbrbk

Manual testing

12927750951020348912074648363807

EC1D0297F318D3__

2020-04-17

Oliver Kruse

Manual testing

12927750951020348912074648363807

F4220E79C5FA22__

2023-05-18

JacobZ

GreatLakes

12927750951020348912074648363807

196480760599294802504182696233054482557605449

F4220E79C5FA2258

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 = 5600000000, B2 = 16709983434234090 (P-1 stage 2)

B1 = 5600000000 (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

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

TF factor-bounds graph:

2⁵⁷

2⁵⁶

2⁵⁴

2⁵³

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=36.04 ~= 103-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

Last modified: 2023-09-25T11:53:03+00:00

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