M91 463 Mersenne number exponent details

is 2 ⁹¹⁴⁶³ - 1

has 27534 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	unknown	1000000000	70552596864750	12,388.9470	67.4908%	12,388.9470	67.4908%
Target	2⁴⁴	0.0000	61.3636%	900	55000	0.0000	3.1795%	0.0000	62.5921%
Difference	-44	0.0000	-61.3636%	+999999100	+70552596809750	+12,388.9470	+64.3112%	+12,388.9470	+4.8987%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
91463	182927	6	17.481	1 1	-	1	1	1.909e-13	3.222e-9	6.558e-9
91463	709973915086262417	18	59.301	3881208330616 2³ × 19 × 83 × 179 × 1718669	2008-08-26	179	1718669	1.0497	0.0003	0.0006
91463	1572636145425012277977176309767	31	100.311	8597116568585178039082341 3 × 7 × 23 × 65203 × 298013 × 916015657393	2019-02-04	298013	916015657393	1.598e+12	160.81	300.35
91463	7918747359850115460397091936427583471385090913607	49	162.438	43289348478893735501771710617558922577354181 3 × 113 × 69191 × 196387 × 358051 × 1696861 × 3966503 × 3899600000939	2022-07-20	3966503	3899600000939	1.443e+12	684.61	1,278.6

exponent	prime factors	composite factor	digits	bits*
91463	182927 709973915086262417	129873398364984725154559	24	76.781
91463	182927 1572636145425012277977176309767	287677612174161220973530930816748009	36	117.792
91463	709973915086262417 1572636145425012277977176309767	1116530641173564700884449196643516827120642126839	49	159.612
91463	182927 709973915086262417 1572636145425012277977176309767	20424360059795667003868963819440860263469770233627 7753	54	177.092
91463	182927 7918747359850115460397091936427583471385090913607	14485526982953020708240588366548885616700605255533 87689	55	179.919
91463	709973915086262417 7918747359850115460397091936427583471385090913607	56221040656517905734931905340633434813760171642754 16841377478008119	67	221.738
91463	182927 709973915086262417 7918747359850115460397091936427583471385090913607	10284346304174850942373888648246052330176706918094 09176542657919591184313	73	239.219
91463	1572636145425012277977176309767 7918747359850115460397091936427583471385090913607	12453308324589178209579431105725841154003898212526 920535656568132279290867299569	80	262.749
91463	182927 1572636145425012277977176309767 7918747359850115460397091936427583471385090913607	22780463318921246023437365938771109447784710883229 11992826049038733453840482508258463	85	280.230
91463	709973915086262417 1572636145425012277977176309767 7918747359850115460397091936427583471385090913607	88415240669849220958130822500070086414411591365116 85302828542615311236259496007830001922084998273	97	322.049
91463	182927 709973915086262417 1572636145425012277977176309767 7918747359850115460397091936427583471385090913607	16173534730013508442207996967470320697529069173646 73057390516814991038515240826224318761601242479085 071	103	339.530

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-12-12	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 182927 skipped known factor: 709973915086262417	-	-	0.656	-	-	40.613%
2022-07-12	George Woltman	SkylakeX	1000000000	70552596864750			7918747359850115460397091936427583471385090913607	49	162.438	12,389	0.000	24,778	67.491%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-04-24	nordi	sweet16	40000000	5240000000	2	7			-	-	1.091
2021-04-30	nordi	sweet16	40000000	5240000000	6	5			-	-	1.091

Trial Factoring results:
No TF results for M91463

ECM factoring results:

Total ECM effort:	14.119 GHz-days
Estimated T-Level:	30.862

Digits	B1	Complete	FacMiss
20	11000	87.991	0.000%
25	50000	14.026	0.000%
30	250000	1.714	18.016%
35	1000000	0.172	84.167%
40	3000000	0.015	98.533%
45	11000000	0.001	99.890%

ECM Summary

B1	B2	factor	curves	GHz-days
		709973915086262417	1	0.00000e+0
11000	1100000		30	0.015
50000	5000000		274	0.636
250000	25000000		585	6.786
1000000	100000000		141	6.543
1000000	100000000	1572636145425012277977176309767	3	0.139

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			709973915086262417	59.301		1		1	-
2009-08-14	Matthias Wurtinger	WUR_E6600	11000	1100000						30	0.015
2011-01-06	James Hintz	NEW_OMFG	50000	5000000						3	0.007
2011-01-18	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2011-01-27	James Hintz	OMFG	50000	5000000						9	0.021
2011-02-17	James Hintz	NEW_OMFG	50000	5000000						10	0.023
2011-02-23	James Hintz	NEW_OMFG	50000	5000000						10	0.023
2011-04-30	James Hintz	NEW_OMFG	50000	5000000						50	0.116
2014-07-06	TJAOI	Manual testing	50000	5000000						181	0.420
2017-01-06	TJAOI	Manual testing	250000	25000000						44	0.510
2017-03-27	kkmrkkblmbrbk	x116xl	250000	25000000						541	6.276
2018-12-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-01-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-01-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000	1572636145425012277977176309767	100.311	3	2		3	0.139
2019-02-10	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-06	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-16	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-29	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M91463

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

182927

709973915086262417

FAA2C79E488BC6__

2017-09-21

Oliver Kruse

Manual testing

182927

709973915086262417

FAA2C79E488BC6__

2017-10-13

kkmrkkblmbrbk

Manual testing

182927

709973915086262417

FAA2C79E488BC6__

2019-02-05

J.R. Allen

aofafujitsu

182927

709973915086262417

1572636145425012277977176309767

0A5496D05F56C733

2019-02-06

kkmrkkblmbrbk

c5.large

182927

709973915086262417

1572636145425012277977176309767

0A5496D05F56C733

2022-05-12

Jorge Coveiro

Manual testing

182927

0A5496D05F56C733

2022-07-20

George Woltman

Manual testing

182927

709973915086262417

1572636145425012277977176309767

7918747359850115460397091936427583471385090913607

0A5496D05F56C733

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 = 1000000000, B2 = 70552596864750 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 100000000, B2 = 2000000000 (P-1 stage 2)

B1 = 100000000 (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:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=30.86 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

2¹⁶⁰

2¹⁷⁰

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