M3288023 Mersenne number exponent details

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M3288023

<<<

>>>

is 2 ^3288023 - 1

has 989794 decimal digits

takes 0.345 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- 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	Prob over default TF
Actual	2⁶⁹	36.3096	68.1159%	3288023	3334803780	28.1430	11.7315%	64.4526	71.8564%	3.7405%
PrimeNet	2⁶⁰	0.0467	63.3333%	14000	260000	0.0042	2.7766%	0.0509	64.3514%	1.0181%
GPU72	2⁶⁴	1.0825	65.6250%	17000	280000	0.0048	1.6881%	1.0873	66.2053%	0.5803%
Difference	+5	+35.2271	+2.4909%	+3271023	+3334523780	+28.1382	+10.0435%	+63.3653	+5.6512%	+5.6512%

Known prime factors (4 factors, 211.1 bits, 0.00641976% 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
3288023	1893901249	10	30.819	288 2⁵ × 3²	-	9	9	4.622e-11	1.371e-6	2.789e-6
3288023	667756285523903	15	49.246	101543737 17 × 5973161	2014-04-25	17	5973161	2.655e-5	0.0496	0.0926
3288023	9829696393604780431	19	63.092	1494773058705 3 × 5 × 99651537247	2016-12-13	5	99651537247	0.5455	826.83	1,544.3
3288023	280434636426134295409	21	67.926	42644871466248 2³ × 3 × 37501 × 47381927	2018-09-25	37501	47381927	12.319	0.3985	0.7343

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3288023	1893901249 667756285523903	1264664463181320511054847	25	80.065
3288023	1893901249 9829696393604780431	18616474277138889270641658319	29	93.911
3288023	1893901249 280434636426134295409	531115508190316638316840065841	30	98.745
3288023	667756285523903 9829696393604780431	6563841551621233368543984117142193	34	112.338
3288023	667756285523903 280434636426134295409	187261991152161661340967431332661327	36	117.173
3288023	9829696393604780431 280434636426134295409	2756587334319840074800569558578336341279	40	131.018
3288023	1893901249 667756285523903 9829696393604780431	12431267712853551851605928830891761633299057	44	143.157
3288023	1893901249 667756285523903 280434636426134295409	354655718933305919463573233069249021699297423	45	147.991
3288023	1893901249 9829696393604780431 280434636426134295409	5220704195445925683145052112902889861090388357471	49	161.837
3288023	667756285523903 9829696393604780431 280434636426134295409	18407285190876537843551176190286025501808233327200 91937	55	180.264
3288023	1893901249 667756285523903 9829696393604780431 280434636426134295409	34861580413700278426697339182201765365120464856869 24686879129313	64	211.083

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-07-02T19:41:01	Jocelyn Larouche	Manual testing	350720	6576046	6	-	skipped known factor: 1893901249 skipped known factor: 667756285523903	-	-	0.105	-	-	3.622%
2021-09-11T10:41:46	Jocelyn Larouche	Manual testing	3288023	3288023		-	skipped known factor: 1893901249	-	-	0.501	-	-	3.493%
2021-09-16T01:49:36	Jocelyn Larouche	Manual testing	3288023	13152092	12	-	skipped known factor: 1893901249 skipped known factor: 667756285523903	-	-	0.583	-	-	5.108%
2021-11-02T11:00:12	Jocelyn Larouche	Manual testing	3288023	131520920	12	-	skipped known factor: 1893901249 skipped known factor: 667756285523903 skipped known factor: 280434636426134295409	-	-	1.565	-	-	7.843%
2022-03-21T14:13:17	Jocelyn Larouche	Manual testing	3288023	1021782300		-	skipped known factor: 1893901249 skipped known factor: 667756285523903 skipped known factor: 280434636426134295409	-	-	8.951	-	-	10.309%
2022-07-25T15:12:26	Jocelyn Larouche	Manual testing	3288023	3334803780		-	skipped known factor: 1893901249 skipped known factor: 667756285523903 skipped known factor: 280434636426134295409	-	-	28.14	-	-	11.732%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-04-25T10:33:00	TJAOI	Manual testing	?	?	667756285523903	49.246	15	3.73725e-6	0.747	8.08914e-6
2016-12-12T17:31:44	TJAOI	Manual testing	2⁶³	2⁶⁴*	9829696393604780431	63.092	19	0.060	0.701	0.122
2021-01-02T03:20:59	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵		-	-	1.136	-	-
2021-01-20T09:17:52	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.273	-	-
2021-01-28T15:12:34	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.545	-	-
2022-03-08T00:19:47	LordJulius	Manual testing	2⁶⁷	2⁶⁸	280434636426134295409	67.926	21	3.282	0.701	6.661
2021-08-29T21:24:46	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.18	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.437 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.437 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	280434636426134295409	3	0.437

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-09-26T01:58:32	ATH	ec2-ECMCF	50000	5000000	280434636426134295409	67.926	3	2		3	0.437

Lucas-Lehmer results:
No L-L results for M3288023

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-03T14:41:21

Oliver Kruse

GTX-0

1893901249

667756285523903

9829696393604780431

373D5223BD0753__

2017-12-14T10:49:30

kkmrkkblmbrbk

c4.xlarge

1893901249

667756285523903

9829696393604780431

373D5223BD0753__

2018-09-26T09:41:18

Oliver Kruse

GTX-2

1893901249

667756285523903

9829696393604780431

280434636426134295409

373D5223BD0753__

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 = 3288023, B2 = 3334803780 (P-1 stage 2)

B1 = 3288023, B2 = 1021782300 (P-1 stage 2)

B1 = 3288023, B2 = 131520920 (P-1 stage 2)

B1 = 3288023, B2 = 13152092 (P-1 stage 2)

B1 = 3288023 (P-1 stage 1)

B1 = 350720, B2 = 6576046 (P-1 stage 2)

B1 = 350720 (P-1 stage 1)

10⁰

10¹

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10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-07-25T15:12:26+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