M258 067 Mersenne number exponent details

is 2 ²⁵⁸⁰⁶⁷ - 1

has 77686 decimal digits

takes 0.002 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	115.1403	73.1343%	30000000	10035812696910	5,417.9473	23.4475%	5,533.0876	79.4337%
Target	2⁴⁴	0.0000	59.0909%	4500	600000	0.0004	10.3896%	0.0004	63.3412%
Difference	+23	+115.1403	+14.0434%	+29995500	+10035812096910	+5,417.9469	+13.0579%	+5,533.0872	+16.0924%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
258067	12387217	8	23.562	24 2³ × 3	-	8	8	4.353e-12	7.927e-8	1.613e-7
258067	4487182285489	13	42.029	8693832 2³ × 3 × 7 × 51749	2008-07-21	8	51749	4.045e-6	2.801e-5	5.217e-5
258067	23077783186543230816122191	26	84.255	44712774563472336285 3³ × 5 × 521 × 635711588305571	2015-09-04	521	635711588305571	23,413,168	343,178	640,962
258067	8352644876596511857258031242507665525809	40	132.617	16183093686129012731689893017138312 2³ × 4651 × 59069 × 115499 × 21380729 × 2981706350261	2022-04-29	21380729	2981706350261	6.123e+11	1,609.8	3,006.3

exponent	prime factors	composite factor	digits	bits*
258067	12387217 4487182285489	55583700688908194113	20	65.591
258067	12387217 23077783186543230816122191	285869508210662480000392678432447	33	107.817
258067	4487182285489 23077783186543230816122191	103554219903012671682989227719670186399	39	126.284
258067	12387217 4487182285489 23077783186543230816122191	1282748593204336917886942772425969767354861583	46	149.846
258067	12387217 8352644876596511857258031242507665525809	103466024610339213818928257993722077031615183553	48	156.180
258067	4487182285489 8352644876596511857258031242507665525809	37479840127244322443336380763556113001701603535685 601	53	174.646
258067	12387217 4487182285489 8352644876596511857258031242507665525809	46427091278148303412357795251279526342859913224450 4783362417	60	198.209
258067	23077783186543230816122191 8352644876596511857258031242507665525809	19276052749628544033877138594089425216239793837286 7546288408127519	66	216.872
258067	12387217 23077783186543230816122191 8352644876596511857258031242507665525809	23877664831309544434169146710406062755883425029773 37208132056060141524623	73	240.434
258067	4487182285489 23077783186543230816122191 8352644876596511857258031242507665525809	86495162432284732913724294198453795308653226149466 5570221094680788309375271791	78	258.901
258067	12387217 4487182285489 23077783186543230816122191 8352644876596511857258031242507665525809	10714343464989587923893451104080882269618694900635 166760757437788470519294626109095647	86	282.463

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-21	Oliver Kruse	Ollaptop	30000000	3000000000	24	-	skipped known factor: 12387217 skipped known factor: 4487182285489	-	-	1.901	-	-	12.598%
2022-04-29	Oliver Kruse	Threadripper-PC	30000000	10035812696910			8352644876596511857258031242507665525809	40	132.617	5,418	0.004	10,836	23.447%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-21	J Feitsma	Manual testing	?	?	4487182285489	42.029	13	1.77499e-6	0.004	3.66220e-6

ECM factoring results:

Total ECM effort:	139.934 GHz-days
Estimated T-Level:	29.832

Digits	B1	Complete	FacMiss
20	11000	48.997	0.000%
25	50000	7.859	0.039%
30	250000	0.966	38.046%
35	1000000	0.099	90.616%
40	3000000	0.009	99.138%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		233	1.698
50000	5000000	23077783186543230816122191	47	0.343
250000	25000000		217	7.908
250000	35250000		8	0.331
250000	36464191		7	0.294
250000	36750000		28	1.180
250000	38500000		42	1.805
1250000	4962067110		50	126.4

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-09-15	TJAOI	Manual testing	50000	5000000						50	0.364
2015-01-23	TJAOI	Manual testing	50000	5000000						50	0.364
2015-09-04	TJAOI	Manual testing	50000	5000000						43	0.313
2015-09-04	TJAOI	Manual testing	50000	5000000	23077783186543230816122191	84.255	47	2		47	0.343
2015-09-18	TJAOI	Manual testing	50000	5000000						90	0.656
2017-05-12	TJAOI	Manual testing	250000	25000000						44	1.603
2020-01-10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-12	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-14	kracker	O0	250000	25000000						3	0.109
2020-01-16	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-19	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-21	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-28	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-31	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-03	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-06	kracker	O0	250000	25000000						3	0.109
2020-02-09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-13	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-20	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-24	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-27	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.109
2020-03-02	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-06	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-12	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-18	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-27	MarkS	desktop-i7	250000	25000000						3	0.109
2020-04-14	Oliver Kruse	Melissa	250000	25000000						3	0.109
2020-04-30	Greg	azure	250000	25000000						3	0.109
2020-05-06	Oliver Kruse	IOS-2	250000	25000000						3	0.109
2020-05-14	nordi	sweet16	250000	25000000						3	0.109
2020-06-01	kracker	O0	250000	25000000						3	0.109
2020-06-15	TJAOI	Manual testing	250000	25000000						19	0.692
2020-10-11	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2020-11-01	nordi	sweet16	250000	25000000						7	0.255
2020-11-29	nordi	sweet16	250000	25000000						7	0.255
2021-01-20	Poao	justg-ZA	250000	25000000						7	0.255
2021-02-14	mnd9	consult	250000	25000000						7	0.255
2021-04-13	Poao	justg-ZA	250000	25000000						7	0.255
2021-05-22	ZacHFX	5950X	250000	38500000						7	0.301
2021-07-25	Team_Inspector	SpudBoy4	250000	38500000						7	0.301
2021-08-23	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2021-09-25	happy5214	Focus	250000	38500000						7	0.301
2021-11-08	mnd9	f4	250000	25000000						7	0.255
2022-01-22	Dylan Delgado	colab	250000	38500000						7	0.301
2022-03-23	Dylan Delgado	colab	250000	38500000						7	0.301
2022-05-19	Dylan Delgado	desktoplinux	250000	38500000						7	0.301
2022-06-15	debrouxl	dl380g9-1	250000	36750000						7	0.295
2022-07-13	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.255
2022-08-07	debrouxl	dl380g9-1	250000	36750000						7	0.295
2022-09-11	debrouxl	o9020	250000	36750000						7	0.295
2022-10-09	Corey	tab	250000	25000000						7	0.255
2022-10-31	debrouxl	z400	250000	36464191						7	0.294
2022-12-04	debrouxl	dl380g9-1	250000	36750000						7	0.295
2023-01-19	TBB_Nozomi	2310m	250000	35250000						8	0.331
2023-06-07	Haruka	server	1250000	4962067110						50	126.4

Lucas-Lehmer results:
No L-L results for M258067

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22

Oliver Kruse

Ollaptop

464E1EFCFB839B__

2017-09-22

Oliver Kruse

Manual testing

464E1EFCFB839B__

2017-10-12

kkmrkkblmbrbk

c4.xlarge

464E1EFCFB839B__

2020-04-17

Oliver Kruse

AddPrpType5

12387217

4487182285489

23077783186543230816122191

2C0BA0DB4338F2__

2022-04-29

aperson1

2012_VP113

12387217

4487182285489

23077783186543230816122191

8352644876596511857258031242507665525809

2C0BA0DB4338F277

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 = 30000000, B2 = 10035812696910 (P-1 stage 2)

B1 = 30000000, B2 = 3000000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=29.83 ~= 82-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

JSON version of this page

Last modified: 2023-10-02T12:12:48+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