M275059 Mersenne number exponent details

is 2 ²⁷⁵⁰⁵⁹ - 1

has 82802 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	Prob over default TF
Actual	unknown	1000000	103121878860	55.6780	59.8315%	55.6780	59.8315%	59.8315%
PrimeNet	2⁴⁰	0.0000	52.5000%	2800	80000	0.0001	14.8657%	0.0001	59.5612%	7.0612%
GPU72	2⁴⁴	0.0000	56.8182%	5000	130000	0.0001	10.8105%	0.0001	61.4863%	4.6682%
Difference	-44	0.0000	-56.8182%	+995000	+103121748860	+55.6779	+49.0210%	+55.6779	-1.6549%	-1.6549%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
275059	166107579983	12	37.273	301949 301949	-	1	301949	9.032e-8	0.0002	0.0003
275059	36198741072395683263274697	26	84.904	65801775387090920972 2² × 409 × 23616251 × 1703112577	2020-06-12	23616251	1703112577	16,932,164	1.1406	1.7172
275059	7333838798655543655598724569	28	92.567	13331392171598718194276 2² × 13 × 9207449 × 27844077808837	2017-09-29	9207449	27844077808837	5.159e+9	15,031	28,074
275059	10751395260489374823799324639	29	93.119	19543798349607492981141 3 × 11 × 7823 × 109686209 × 690191611	2016-03-04	109686209	690191611	1.235e+10	1.4002	2.2118

exponent	prime factors	composite factor	digits	bits*
275059	166107579983 36198741072395683263274697	6012885277966873151078336178427590151	37	122.177
275059	166107579983 7333838798655543655598724569	1218206214830104350638713347097954702327	40	129.840
275059	166107579983 10751395260489374823799324639	1785888248160585948265912849414075101137	40	130.392
275059	36198741072395683263274697 7333838798655543655598724569	26547573173922144377459318284983633139966219148993 0593	54	177.471
275059	36198741072395683263274697 10751395260489374823799324639	38918697320143701841529392272661248963432902013735 9383	54	178.023
275059	7333838798655543655598724569 10751395260489374823799324639	78848999701058302501391907157839077852840317131976 355591	56	185.685
275059	166107579983 36198741072395683263274697 7333838798655543655598724569	44097531343418177669936974543515732296428681812094 707915866119919	65	214.744
275059	166107579983 36198741072395683263274697 10751395260489374823799324639	64646906279399377106955479179764605564581066135004 441358088030489	65	215.296
275059	166107579983 7333838798655543655598724569 10751395260489374823799324639	13097416524423085072496165187049664829883636881726 847653196881734953	68	222.958
275059	36198741072395683263274697 7333838798655543655598724569 10751395260489374823799324639	28542345239960141261313959241607536386264480346970 37559334485416166297682384780927	82	270.589
275059	166107579983 36198741072395683263274697 7333838798655543655598724569 10751395260489374823799324639	47410998948490784922956869883997258717770099518263 1325560308144515990333505717528013585384241	93	307.863

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-01-03T17:57:47	Lisander Viaene	Manual testing	100000	100000		-		-	-	0.001	-	-	11.645%
2022-04-05T01:03:00	Jocelyn Larouche	Manual testing	1000000	103121878860		-	skipped known factor: 166107579983	-	-	55.68	-	-	49.524%

Trial Factoring results:
No TF results for M275059

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.001 GHz-days
Estimated T-Level:	26.914

Digits	B1	Curves	Complete	FacMiss
20	11000	526 / 100	5.260	0.506%
25	50000	526 / 280	1.879	15.230%
30	250000	245 / 640	0.383	68.174%

New Calculation Method

Total ECM effort:	11.001 GHz-days
Estimated T-Level:	26.914

Digits	B1	Complete	FacMiss
20	11000	29.481	0.000%
25	50000	3.771	2.303%
30	250000	0.369	69.139%
35	1000000	0.029	97.159%
40	3000000	0.002	99.814%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		223	1.629
50000	5000000	10751395260489374823799324639	58	0.424
250000	25000000		205	7.487
250000	25000000	36198741072395683263274697	1	0.037
250000	25000000	7333838798655543655598724569	39	1.424

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-08-28T10:10:00	TJAOI	Manual testing	50000	5000000						50	0.365
2015-01-09T16:38:00	TJAOI	Manual testing	50000	5000000						50	0.365
2015-10-02T10:44:58	TJAOI	Manual testing	50000	5000000						90	0.657
2016-03-04T13:11:55	TJAOI	Manual testing	50000	5000000						33	0.241
2016-03-04T13:11:55	TJAOI	Manual testing	50000	5000000	10751395260489374823799324639	93.119	58	2		58	0.424
2017-09-29T10:31:04	TJAOI	Manual testing	250000	25000000						5	0.183
2017-09-29T10:31:04	TJAOI	Manual testing	250000	25000000	7333838798655543655598724569	92.567	39	2		39	1.424
2020-02-19T01:44:07	MarkS	desktop-i7	250000	25000000						3	0.110
2020-02-22T10:16:34	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.110
2020-02-26T04:30:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.110
2020-02-29T12:05:55	kracker	O0	250000	25000000						3	0.110
2020-03-05T05:50:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.110
2020-03-11T08:20:42	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.110
2020-03-16T11:11:37	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.110
2020-03-21T21:44:25	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.110
2020-04-11T06:16:59	Oliver Kruse	IOS-2	250000	25000000						3	0.110
2020-04-28T09:43:47	Greg	azure3	250000	25000000						3	0.110
2020-05-02T19:02:26	kracker	O0	250000	25000000						3	0.110
2020-05-08T07:37:16	Greg Hogan	azure2	250000	25000000						3	0.110
2020-05-26T13:23:11	kracker	O0	250000	25000000						3	0.110
2020-06-12T17:30:32	Chang Chia-Tche	exbpc13	250000	25000000	36198741072395683263274697	84.904	1	2		1	0.037
2020-06-17T05:20:12	nordi	sweet16	250000	25000000						3	0.110
2020-06-27T03:50:29	nordi	sweet16	250000	25000000						3	0.110
2020-07-08T05:14:25	Chang Chia-Tche	exbpc13	250000	25000000						3	0.110
2020-07-21T20:08:33	argusdusty	Argus-PC	250000	25000000						3	0.110
2020-08-03T01:15:00	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.110
2020-09-12T20:53:02	MarkS	laptop64	250000	25000000						7	0.256
2020-10-22T17:00:12	nordi	sweet16	250000	25000000						7	0.256
2020-11-06T12:04:13	nordi	sweet16	250000	25000000						7	0.256
2020-12-28T22:53:17	MarkS	desktop-i7	250000	25000000						101	3.689
2021-03-19T18:31:12	TJAOI	Manual testing	250000	25000000						24	0.877

Lucas-Lehmer results:
No L-L results for M275059

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T10:35:53

Oliver Kruse

Ollaptop

4A8877C8495FC7__

2017-09-22T20:35:46

Oliver Kruse

Manual testing

4A8877C8495FC7__

2017-09-29T12:15:22

Oliver Kruse

GTX-1

166107579983

7333838798655543655598724569

10751395260489374823799324639

E329B30AB0B96767

2017-10-05T21:15:43

Oliver Kruse

Manual testing

166107579983

7333838798655543655598724569

10751395260489374823799324639

E329B30AB0B967__

2017-10-13T05:49:35

Oliver Kruse

Threadripper

15A6E2D1AED8CB__

2017-10-13T05:57:51

Oliver Kruse

GTX-1

E329B30AB0B967__

2017-11-02T10:45:50

kkmrkkblmbrbk

c4.xlarge

166107579983

7333838798655543655598724569

10751395260489374823799324639

15A6E2D1AED8CB__

2019-04-09T05:09:15

kkmrkkblmbrbk

c5.large

166107579983

7333838798655543655598724569

10751395260489374823799324639

E329B30AB0B96767

2020-06-13T09:25:27

LaurV

3tits

166107579983

36198741072395683263274697

7333838798655543655598724569

10751395260489374823799324639

15A6E2D1AED8CBF2

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 = 1000000, B2 = 103121878860 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-05T01:03:00+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