M13 241 Mersenne number exponent details

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M13241

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<<

is 2 ¹³²⁴¹ - 1

has 3986 decimal digits

takes 0.000 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown			8300000000	34023579430740900	530,108.5138	76.5355%	530,108.5138	76.5355%
Target	2⁴⁴	0.0002	68.1818%	500	80000	0.0000	1.3770%	0.0002	68.6200%
Difference	-44	-0.0002	-68.1818%	+8299999500	+34023579430660900	+530,108.5138	+75.1585%	+530,108.5136	+7.9155%

Known prime factors (3 factors, 267.6 bits, 2.02133122% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13241	105929	6	16.693	4 2²	-	4	4	6.599e-13	1.144e-9	2.328e-9
13241	2873428837589316258707742676348894313	37	121.112	108504978384914895351851924943316 2² × 7 × 988359554417 × 3920817866476823891	2023-06-02	988359554417	3920817866476823891	1.343e+13	61,088,788	114,096,344
13241	1217859473761865727563164516097890942633	40	129.840	45988198540966155409831754251865076 2² × 3 × 11 × 59 × 39979 × 1671947 × 2465431 × 35832174887609	2023-05-18	2465431	35832174887609	1.219e+13	558.29	1,042.7

exponent	prime factors	composite factor	digits	bits*
13241	105929 2873428837589316258707742676348894313	304379443336998681968652473962962025681777	42	137.805
13241	105929 1217859473761865727563164516097890942633	129006636196120674655038454025733489662171057	45	146.532
13241	2873428837589316258707742676348894313 1217859473761865727563164516097890942633	34994325320386942412111056765738810019148934420933 34088959193007086862946129	76	250.952
13241	105929 2873428837589316258707742676348894313 1217859473761865727563164516097890942633	37069138868632684227725121321379464065184274742750 4786709358356047704305020498841	81	267.644

4 Composite Factors:

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-02-05	Jocelyn Larouche	Manual testing	1000000	3910366209750		-	skipped known factor: 105929	-	-	60.93	-	-	48.975%
2023-05-17	JacobZ	GreatLakes	8300000000	34023579430740900			1217859473761865727563164516097890942633	40	129.840	530,109	5.22284e-6	1,060,217	76.536%

Trial Factoring results:
No TF results for M13241

ECM factoring results:

Total ECM effort:	359.864 GHz-days
Estimated T-Level:	39.289

Digits	B1	Complete	FacMiss
20	11000	958.933	0.000%
25	50000	219.283	0.000%
30	250000	42.669	0.000%
35	1000000	6.620	0.133%
40	3000000	0.858	42.413%
45	11000000	0.095	90.922%
50	44000000	0.009	99.074%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		148	0.030
250000	25000000		551	0.567
500000	50000000		10	0.021
1000000	100000000		1,421	5.848
3000000	300000000		312	3.852
3000000	528000000		1,000	15.40
3000000	22972799850		1,000	315.8
3000000	22972799850	2873428837589316258707742676348894313	58	18.32

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-07	Matthias Wurtinger	AMD_Funzel	50000	5000000						50	0.010
2009-06-07	unconnected	dual5430	250000	25000000						30	0.031
2009-06-09	Rob_Dee	twopc	50000	5000000						80	0.016
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-08	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-09	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-21	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-24	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-28	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-31	Rob_Dee	twopc	500000	50000000						5	0.010
2009-08-10	Rob_Dee	twopc	500000	50000000						5	0.010
2010-05-24	James Hintz	home2	250000	25000000						481	0.495
2010-12-30	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-08	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-11	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-14	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-17	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-20	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-23	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-27	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-30	James Hintz	newestmember	1000000	100000000						3	0.012
2011-03-30	James Hintz	newestmember	1000000	100000000						3	0.012
2011-04-11	James Hintz	17_051310	1000000	100000000						11	0.045
2017-05-07	kkmrkkblmbrbk	c4.large	1000000	100000000						1380	5.679
2019-02-15	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-17	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-02-19	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-02-23	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-02-25	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-02-27	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-01	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-03	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-05	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-07	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-08	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-09	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-11	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-13	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-15	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-17	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-22	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-27	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-28	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-30	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-01	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-03	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-05	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-07	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-09	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-11	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-14	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-18	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-26	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-28	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-01	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-04	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-06	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-08	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-11	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-13	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-15	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-18	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-25	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-29	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-02	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-05	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-09	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-12	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-16	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-23	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-27	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-07-05	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-19	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-07-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-04	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-13	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-25	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-22	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-30	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-12	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-16	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-19	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-24	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-31	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-02	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2021-09-12	nordi	sweet16	3000000	528000000						1000	15.40
2023-06-02	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-02	Denial140	i5-8400	3000000	22972799850	2873428837589316258707742676348894313	121.112	58	2	3298178312076504	58	18.32
2023-06-02	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-02	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-02	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-02	Denial140	i5-8400	3000000	22972799850						200	63.17

Lucas-Lehmer results:
No L-L results for M13241

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

105929

5D9DDAD0F07F5F__

no

2017-09-21

Oliver Kruse

Manual testing

105929

5D9DDAD0F07F5F__

no

2017-10-12

kkmrkkblmbrbk

Manual testing

105929

5D9DDAD0F07F5F__

no

2020-04-17

Oliver Kruse

Manual testing

105929

D76B3E51380650__

no

2023-05-17

JacobZ

GreatLakes

105929

1217859473761865727563164516097890942633

D76B3E51380650E9

no

2023-06-02

Denial140

i5-8400

105929

2873428837589316258707742676348894313

1217859473761865727563164516097890942633

D76B3E51380650E9

no

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 = 8300000000, B2 = 34023579430740900 (P-1 stage 2)

B1 = 1000000, B2 = 3910366209750 (P-1 stage 2)

B1 = 8300000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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10⁸

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10¹⁰

10¹¹

10¹²

10¹³

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10¹⁶

10¹⁷

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10¹⁹

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=39.29 ~= 114-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

Last modified: 2023-07-11T14:45:05+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