M1669597 Mersenne number exponent details

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M1669597

<<<

>>>

is 2 ^1669597 - 1

has 502599 decimal digits

takes 0.079 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	17.7971	68.6567%	500000	15000000	0.0880	5.0128%	17.8851	70.2279%	1.5712%
PrimeNet	2⁵⁷	0.0115	63.1579%	7000	120000	0.0009	2.5694%	0.0124	64.1045%	0.9466%
GPU72	2⁶¹	0.1840	65.5738%	7000	80000	0.0007	1.2067%	0.1847	65.9892%	0.4154%
Difference	+6	+17.6131	+3.0829%	+493000	+14920000	+0.0873	+3.8061%	+17.7004	+4.2387%	+4.2387%

Known prime factors (4 factors, 195.2 bits, 0.01168868% 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
1669597	16869608089	11	33.974	5052 2² × 3 × 421	-	4	421	7.495e-10	1.823e-6	2.920e-6
1669597	3132057117793	13	41.510	937968 2⁴ × 3 × 19541	2008-07-15	16	19541	1.796e-7	7.368e-5	0.0001
1669597	13834768077329137	17	53.619	4143145944 2³ × 3 × 7 × 313 × 78791	2014-10-02	313	78791	0.0013	0.0003	0.0005
1669597	76428953397207154607	20	66.051	22888443557699 59077 × 387434087	2019-03-14	59077	387434087	11.285	1.4443	2.6904

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1669597	16869608089 3132057117793	52836576089530818627577	23	75.484
1669597	16869608089 13834768077329137	233387115466750587050589193	27	87.593
1669597	3132057117793 13834768077329137	43331283829614100977640034641	29	95.129
1669597	16869608089 76428953397207154607	1289326490463329845366920816023	31	100.024
1669597	3132057117793 76428953397207154607	239379847493192156554158961622351	33	107.561
1669597	13834768077329137 76428953397207154607	1057376844643357839947223651984884159	37	119.670
1669597	16869608089 3132057117793 13834768077329137	730981776198812935600859136510053811049	39	129.103
1669597	16869608089 3132057117793 76428953397207154607	4038244211614740776637394385576252992797239	43	141.535
1669597	16869608089 13834768077329137 76428953397207154607	17837532971516885736895251452616322714394362151	47	153.644
1669597	3132057117793 13834768077329137 76428953397207154607	3311764672454732087186631510668135962640522741087	49	161.180
1669597	16869608089 3132057117793 13834768077329137 76428953397207154607	55868172107306783904331452185029476229912364232229 707852743	59	195.154

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:10	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 16869608089 skipped known factor: 3132057117793 skipped known factor: 13834768077329137	-	-	0.088	-	-	5.013%

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	?	?	3132057117793	41.510	13	4.10170e-9	0.171	8.93853e-9
2014-10-02T11:33:00	TJAOI	Manual testing	2⁵³	2⁵⁴*	13834768077329137	53.619	17	0.001	0.170	0.001

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.891 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.891 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	14.83
50000	5000000	76428953397207154607	1	0.059

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-08-07T18:13:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-01-30T15:09:14	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-03-14T18:37:51	Chang Chia-Tche	exbpc13	50000	5000000	76428953397207154607	66.051	1	2		1	0.059
2019-12-09T17:17:26	TJAOI	Manual testing	50000	5000000						246	14.59

Lucas-Lehmer results:
No L-L results for M1669597

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T14:59:24

alpertron

Manual testing

16869608089

3132057117793

13834768077329137

E78DD4DDF4D5AF__

2017-10-18T12:39:10

Oliver Kruse

Threadripper

16869608089

3132057117793

13834768077329137

E78DD4DDF4D5AF__

2019-03-24T00:10:50

ANONYMOUS

dory

16869608089

3132057117793

13834768077329137

76428953397207154607

0FECA5BE83861A6A

2019-03-24T19:48:16

Justine V.

Gible_Desktop_1

16869608089

3132057117793

13834768077329137

76428953397207154607

0FECA5BE83861A6A

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

10⁹

TF factor-bounds graph:

2⁶⁷

2⁵⁴

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-12-09T17:17:26+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