M21017 Mersenne number exponent details

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M21017

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is 2 ²¹⁰¹⁷ - 1

has 6327 decimal digits

takes 0.000 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	1,413.8039	77.6119%	500000000	10000000000	0.4722	13.3830%	1,414.2761	80.6081%	2.9962%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	3.7444%	0.0000	63.9041%	1.4041%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.5827%	0.0001	66.4486%	0.5395%
Difference	+23	+1,413.8038	+11.7028%	+499999500	+9999990000	+0.4722	+11.8003%	+1,414.2760	+14.1595%	+14.1595%

Known prime factors (1 factor, 89.1 bits, 0.42398413% 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
21017	667428753559725097403041687	27	89.109	15878306931525077256579 3 × 5292768977175025752193	2014-04-23	3	5292768977175025752193	1.051e+10	1.338e+11	2.499e+11

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-04-29T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.000	-	-	1.842%
2001-08-18T00:00:00	Alex Kruppa	v4_computers	1000000	100000000		-		-	-	0.003	-	-	4.561%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	4.86067e-5	-	-	0.604%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	9.72135e-5	-	-	0.981%
2002-07-20T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.000	-	-	1.478%
2003-02-02T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.000	-	-	2.099%
2003-03-27T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.001	-	-	2.837%
2003-04-03T00:00:00	ANONYMOUS	v4_computers	524288	52428800		-		-	-	0.002	-	-	3.683%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	1048576	104857600		-		-	-	0.003	-	-	4.628%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2097152	209715200		-		-	-	0.006	-	-	5.665%
2003-07-06T00:00:00	ANONYMOUS	v4_computers	4194304	419430400		-		-	-	0.012	-	-	6.787%
2003-09-29T00:00:00	ANONYMOUS	v4_computers	8388608	838860800		-		-	-	0.025	-	-	7.989%
2003-09-29T00:00:00	ANONYMOUS	v4_computers	16777216	1677721600		-		-	-	0.050	-	-	9.256%
2016-11-19T00:49:55	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-		-	-	0.472	-	-	13.383%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-11-28T00:00:00	eteo	v4_computers	?	?	667428753559725097403041687	89.109	27	4.54367e+9	1.39230e-5	9.40632e+9
1999-10-15T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.029	-	-
2000-03-01T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.057	-	-
2000-08-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.457	-	-
2002-11-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.913	-	-
2022-06-16T04:12:24	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.913	-	-
2022-06-16T04:12:24	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	1.827	-	-
2022-06-16T04:12:24	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	3.654	-	-
2022-06-15T12:26:39	LordJulius	Whitebox_TF	2⁵⁹	2⁶⁰		-	-	3.654	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	41.138 GHz-days
Estimated T-Level:	36.678

Digits	B1	Curves	Complete	FacMiss
20	11000	3546 / 100	35.460	0.000%
25	50000	3546 / 280	12.664	0.000%
30	250000	3416 / 640	5.338	0.479%
35	1000000	2961 / 1566	1.891	15.086%
40	3000000	1540 / 4588	0.336	71.484%

New Calculation Method

Total ECM effort:	41.138 GHz-days
Estimated T-Level:	36.678

Digits	B1	Complete	FacMiss
20	11000	591.197	0.000%
25	50000	135.290	0.000%
30	250000	24.272	0.000%
35	1000000	3.557	2.852%
40	3000000	0.435	64.723%
45	11000000	0.046	95.472%
50	44000000	0.004	99.570%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	130	0.043
250000	25000000	455	0.759
1000000	100000000	1,421	9.488
3000000	300000000	1,540	30.85

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-03T13:21:00	Matthias Wurtinger	AMD_Funzel	50000	5000000						30	0.010
2009-06-01T18:13:00	GrunwalderGIMP	GWPrime02	50000	5000000						100	0.033
2009-06-12T19:41:00	unconnected	dual5430	250000	25000000						30	0.050
2011-04-01T18:50:00	James Hintz	17_051310	250000	25000000						11	0.018
2014-10-09T00:33:00	James Hintz	08_04_2014	250000	25000000						414	0.691
2014-10-09T00:51:00	James Hintz	08_04_2014	1000000	100000000						11	0.073
2017-10-08T20:35:09	kkmrkkblmbrbk	r4.4xlarge-8	1000000	100000000						1410	9.414
2021-10-14T08:27:55	nordi	sweet16	3000000	300000000						400	8.012
2022-02-01T06:41:09	fbaur	Manual testing	3000000	300000000						380	7.612
2022-02-01T06:41:10	fbaur	Manual testing	3000000	300000000						380	7.612
2022-02-01T08:21:56	fbaur	Manual testing	3000000	300000000						380	7.612

Lucas-Lehmer results:
No L-L results for M21017

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:26:18

Oliver Kruse

Oliver-PC

667428753559725097403041687

8BC5A0B600036B__

2017-09-21T20:26:58

Oliver Kruse

Manual testing

667428753559725097403041687

8BC5A0B600036B__

2017-10-12T16:29:43

kkmrkkblmbrbk

Manual testing

667428753559725097403041687

8BC5A0B600036B__

2020-04-17T13:48:58

Oliver Kruse

Manual testing

667428753559725097403041687

D6D02190257876__

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

B1 = 16777216, B2 = 1677721600 (P-1 stage 2)

B1 = 8388608, B2 = 838860800 (P-1 stage 2)

B1 = 4194304, B2 = 419430400 (P-1 stage 2)

B1 = 16777216 (P-1 stage 1)

B1 = 2097152, B2 = 209715200 (P-1 stage 2)

B1 = 8388608 (P-1 stage 1)

B1 = 1048576, B2 = 104857600 (P-1 stage 2)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 4194304 (P-1 stage 1)

B1 = 524288, B2 = 52428800 (P-1 stage 2)

B1 = 2097152 (P-1 stage 1)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 1048576 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 524288 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10⁰

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10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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10²⁰

10²¹

10²²

TF factor-bounds graph:

2⁶⁷

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁴

2⁵³

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-06-16T04:12:24+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