M1704041 Mersenne number exponent details

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M1704041

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>>>

is 2 ^1704041 - 1

has 512968 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	17.4373	68.6567%	3000000	273000000	1.2086	9.5062%	18.6459	71.6363%	2.9795%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7325%	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	+17.2571	+3.0829%	+2993000	+272900000	+1.2077	+8.2042%	+18.4648	+5.6143%	+5.6143%

Known prime factors (3 factors, 143.6 bits, 0.00842439% 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
1704041	167606064679	12	37.286	49179 3 × 13² × 97	-	169	169	1.767e-8	1.153e-5	2.347e-5
1704041	375229828201	12	38.449	110100 2² × 3 × 5² × 367	2008-07-15	25	367	3.935e-8	2.978e-6	3.472e-6
1704041	260489222350085594783	21	67.820	76432791919351 7 × 10918970274193	2019-05-07	7	10918970274193	32.135	40,596	75,822

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1704041	167606064679 375229828201	62890794854946864212479	23	75.735
1704041	167606064679 260489222350085594783	43659573449390858580385682969657	32	105.106
1704041	375229828201 260489222350085594783	97743326150634707208069991875383	32	106.269
1704041	167606064679 375229828201 260489222350085594783	16382374244743872833218006569024447605897057	44	143.555

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: 167606064679 skipped known factor: 375229828201	-	-	0.088	-	-	5.025%
2021-04-07T07:18:37	Dylan Delgado	laptop-i78750	1000000	69000000		-	skipped known factor: 167606064679 skipped known factor: 375229828201	-	-	0.321	-	-	7.046%
2021-07-21T18:18:29	Dylan Delgado	laptop-ryzen73700	3000000	273000000		-	skipped known factor: 167606064679 skipped known factor: 375229828201	-	-	1.209	-	-	9.506%

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	?	?	375229828201	38.449	12	1.78613e-8	0.174	3.88217e-8

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	8.290	0.025%
25	50000	0.749	47.271%
30	250000	0.046	95.491%
35	1000000	0.002	99.789%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		254	15.10
50000	5000000	260489222350085594783	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-05-17T04:41:40	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-07T10:09:54	Ismo Laitela	6600K	50000	5000000						3	0.178
2019-05-07T20:50:12	Chang Chia-Tche	exbpc13	50000	5000000	260489222350085594783	67.820	3	2		3	0.178
2020-02-02T21:14:09	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-10T05:22:39	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-03T14:21:42	TJAOI	Manual testing	50000	5000000						244	14.51

Lucas-Lehmer results:
No L-L results for M1704041

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:15:09

alpertron

Manual testing

167606064679

375229828201

37B5E4BFAAA9F4__

2017-10-18T19:14:40

Oliver Kruse

Threadripper

167606064679

375229828201

37B5E4BFAAA9F4__

2019-05-08T19:15:01

artorollo

fourth

167606064679

375229828201

260489222350085594783

0D578E676D5593B4

2019-05-09T16:40:54

kkmrkkblmbrbk

c5.large

167606064679

375229828201

260489222350085594783

0D578E676D5593B4

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 = 3000000, B2 = 273000000 (P-1 stage 2)

B1 = 1000000, B2 = 69000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-07-21T18:18:29+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