M1667873 Mersenne number exponent details

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M1667873

<<<

>>>

is 2 ^1667873 - 1

has 502080 decimal digits

takes 0.078 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	967CCF4893FE1C44	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	35.7371	69.1176%	25000000	556762626420	2,071.6217	20.7199%	2,107.3588	75.5164%
Target	2⁶¹	0.1842	65.5738%	7000	80000	0.0007	1.2064%	0.1849	65.9891%
Difference	+7	+35.5529	+3.5439%	+24993000	+556762546420	+2,071.6210	+19.5135%	+2,107.1739	+9.5273%

Known prime factors (1 factor, 125.5 bits, 0.00752671% 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
1667873	61669335183201555395946715736375580503	38	125.536	18487419360827099963830194426187 7 × 37 × 251 × 2251 × 550757 × 7085809 × 32372619661	2023-01-08	7085809	32372619661	1.015e+11	120.82	224.80

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.763%
2012-02-29	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.126%
2012-02-29	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.381%
2012-02-29	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.582%
2012-02-29	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.749%
2012-02-29	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	1.892%
2012-02-29	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.019%
2012-02-29	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.132%
2012-02-29	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.235%
2012-02-29	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.329%
2012-03-01	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.298%
2012-03-01	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.194%
2018-01-22	Jocelyn Larouche	low 4M	1667873	20000000	12	-		-	-	0.182	-	-	5.434%
2018-02-04	Jocelyn Larouche	low 4M	1667873	40000000	12	-		-	-	0.256	-	-	6.184%
2018-02-21	Jocelyn Larouche	low 4M	1667873	80000000	12	-		-	-	0.405	-	-	6.944%
2018-05-22	VictordeHollander	Manual testing	10000000	200000000	12	-		-	-	1.389	-	-	9.093%
2023-01-03	Jocelyn Larouche	Manual testing	1668873	1152946410		-		-	-	4.394	-	-	9.935%
2023-01-08	Naegi Makoto	5950X	25000000	556762626420			61669335183201555395946715736375580503	38	125.536	2,072	0.157	4,143	20.720%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2001-12-01	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁷	2⁶⁰		-	-	0.081	-	-
2010-04-29	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.092	-	-
2016-02-23	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.184	-	-
2010-08-22	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.957	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.589	-	-
2015-05-11	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.177	-	-
2015-05-12	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.240	-	-
2015-10-11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.480	-	-
2017-09-29	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.961	-	-
2019-07-31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.92	-	-

ECM factoring results:

Total ECM effort:	16.610 GHz-days
Estimated T-Level:	24.982

Digits	B1	Complete	FacMiss
20	11000	10.769	0.002%
25	50000	0.996	36.919%
30	250000	0.063	93.908%
35	1000000	0.003	99.707%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	16.61

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-31	James Heinrich	Q6600	50000	5000000						3	0.178
2009-06-27	James Hintz	20_060209	50000	5000000						3	0.178
2010-05-24	SubPrime	abd0	50000	5000000						3	0.178
2011-10-17	Bud	annan	50000	5000000						3	0.178
2013-03-23	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2013-12-10	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-08-02	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-10-27	mikr	MSI	50000	5000000						12	0.712
2016-05-22	Bruce	DESK3	50000	5000000						3	0.178
2016-08-17	Bruce	DESK3	50000	5000000						3	0.178
2016-10-18	Bruce	DESK3	50000	5000000						3	0.178
2016-12-17	Bruce	DESK3	50000	5000000						3	0.178
2017-03-21	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-09-23	ANONYMOUS	Worker	50000	5000000						3	0.178
2017-12-29	Bruce	DESK3	50000	5000000						3	0.178
2018-02-19	Bruce	DESK3	50000	5000000						3	0.178
2018-06-27	VictordeHollander	Manual testing	50000	5000000						223	13.23

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-21	bezahar	v4_computers	967CCF4893FE1C44	0.078
2015-07-06	MadPoo	Manual testing	967CCF4893FE1C44	0.078

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-01-08

Naegi Makoto

5950X

61669335183201555395946715736375580503

B854540FDA5DE819

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 = 25000000, B2 = 556762626420 (P-1 stage 2)

B1 = 1668873, B2 = 1152946410 (P-1 stage 2)

B1 = 25000000 (P-1 stage 1)

B1 = 10000000, B2 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 1667873, B2 = 80000000 (P-1 stage 2)

B1 = 1667873, B2 = 40000000 (P-1 stage 2)

B1 = 1667873, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1668873 (P-1 stage 1)

B1 = 1667873 (P-1 stage 1)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁸

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

Last modified: 2023-01-08T11:52:14+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