M1704119 Mersenne number exponent details

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M1704119

<<<

>>>

is 2 ^1704119 - 1

has 512991 decimal digits

takes 0.080 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	2⁶⁷	17.4365	68.6567%	500000	15000000	0.0880	5.0252%	17.5246	70.2318%	1.5751%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7326%	0.0123	64.1646%	1.0067%
GPU72	2⁶¹	0.1803	65.5738%	7000	100000	0.0008	1.3020%	0.1811	66.0220%	0.4482%
Difference	+6	+17.2563	+3.0829%	+493000	+14900000	+0.0872	+3.7232%	+17.3435	+4.2098%	+4.2098%

Known prime factors (4 factors, 186.0 bits, 0.01091640% 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
1704119	24978976303	11	34.540	7329 3 × 7 × 349	-	7	349	2.131e-9	1.749e-6	2.394e-6
1704119	1526876991049	13	40.474	447996 2² × 3 × 37 × 1009	2008-07-15	37	1009	1.692e-7	6.139e-6	6.978e-6
1704119	39770565762905521	17	55.143	11668952040 2³ × 3 × 5 × 97241267	2015-01-08	8	97241267	0.0034	0.3615	0.6753
1704119	65944180143955153	17	55.872	19348466904 2³ × 3² × 13 × 17 × 863 × 1409	2015-07-21	863	1409	0.0052	6.092e-5	0.0001

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1704119	24978976303 1526876991049	38139824177008914111847	23	75.014
1704119	24978976303 39770565762905521	993428019748520125486868863	27	89.683
1704119	24978976303 65944180143955153	1647218113136618895481739359	28	90.412
1704119	1526876991049 39770565762905521	60724761784381559044149681529	29	95.616
1704119	1526876991049 65944180143955153	100688651355395455678638425497	30	96.346
1704119	39770565762905521 65944180143955153	2622637353096056879113406000099713	34	111.015
1704119	24978976303 1526876991049 39770565762905521	1516842385617386958874010225697887807287	40	130.156
1704119	24978976303 1526876991049 65944180143955153	2515099436187451918590596013794793997591	40	130.886
1704119	24978976303 39770565762905521 65944180143955153	65510796294349048466113904126108746664101039	44	145.555
1704119	1526876991049 39770565762905521 65944180143955153	4004444630308021091847234888270152379408468937	46	151.488
1704119	24978976303 1526876991049 39770565762905521 65944180143955153	10002692752713965444407626677017498894744321073483 4599911	57	186.028

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:29:38	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 24978976303 skipped known factor: 1526876991049 skipped known factor: 65944180143955153	-	-	0.088	-	-	5.025%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:45:00	J Feitsma	Manual testing	?	?	1526876991049	40.474	13	8.32744e-8	0.174	1.80997e-7
2015-01-08T13:42:00	TJAOI	Manual testing	2⁵⁵	2⁵⁶*	39770565762905521	55.143	17	0.001	0.169	0.001
2015-02-20T12:04:00	TJAOI	Manual testing	2⁵⁵	2⁵⁶*	65944180143955153	55.872	17	0.002	0.169	0.005

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.280 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	15.280 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	9.885	0.005%
25	50000	0.915	40.068%
30	250000	0.058	94.394%
35	1000000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	15.28

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-05-10T08:59:31	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-07T02:16:22	alpertron		50000	5000000						3	0.178
2018-09-28T16:56:59	alpertron	Manual testing	50000	5000000						3	0.178
2020-02-02T21:28:13	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-10T07:21:38	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-03T14:21:43	TJAOI	Manual testing	50000	5000000						244	14.51

Lucas-Lehmer results:
No L-L results for M1704119

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T03:14:16

Oliver Kruse

GTX-0

24978976303

1526876991049

39770565762905521

65944180143955153

0F6AD65A9A435CAF

2017-10-05T21:05:49

Oliver Kruse

Manual testing

24978976303

1526876991049

39770565762905521

65944180143955153

0F6AD65A9A435C__

2017-11-10T13:29:09

kkmrkkblmbrbk

c4.xlarge

24978976303

1526876991049

39770565762905521

65944180143955153

0F6AD65A9A435C__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁵⁶

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-03-03T14:21:43+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