M21011 Mersenne number exponent details

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M21011

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>>>

is 2 ²¹⁰¹¹ - 1

has 6325 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	1,414.2077	77.6119%	500000000	10000000000	0.4722	13.3827%	1,414.6798	80.6081%	2.9961%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	3.7441%	0.0000	63.9040%	1.4040%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.5825%	0.0001	66.4486%	0.5395%
Difference	+23	+1,414.2076	+11.7028%	+499999500	+9999990000	+0.4722	+11.8002%	+1,414.6797	+14.1595%	+14.1595%

Known prime factors (4 factors, 187.6 bits, 0.89273508% 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
21011	42023	5	15.359	1 1	-	1	1	2.078e-13	4.640e-10	9.443e-10
21011	66721060831	11	35.957	1587765 3 × 5 × 151 × 701	2008-08-26	151	701	3.643e-7	8.397e-8	1.426e-7
21011	274998859609	12	38.0006	6544164 2² × 3 × 11² × 4507	2008-08-26	121	4507	2.589e-6	1.670e-7	2.126e-7
21011	378345220325684694558107006777	30	98.256	9003503410729729535912308 2² × 31 × 72608898473626851096067	2014-10-09	31	72608898473626851096067	3.788e+12	1.836e+12	3.428e+12

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
21011	42023 66721060831	2803819139301113	16	51.316
21011	42023 274998859609	11556277077349007	17	53.360
21011	66721060831 274998859609	18348215640427717875079	23	73.958
21011	42023 66721060831 274998859609	771047065857693988264444817	27	89.317
21011	42023 378345220325684694558107006777	15899201193746247919415330745789871	35	113.615
21011	66721060831 378345220325684694558107006777	25243594460468106137337112263375546251687	41	134.213
21011	274998859609 378345220325684694558107006777	104044504128079138575584915049467434570193	42	136.256
21011	42023 66721060831 378345220325684694558107006777	1060811570012251224209317468643830580134642801	46	149.572
21011	42023 274998859609 378345220325684694558107006777	4372262196974269640361804885123770002943220439	46	151.615
21011	66721060831 274998859609 378345220325684694558107006777	69419596890607988200836798084214840761113594924103 83	52	172.214
21011	42023 66721060831 274998859609 378345220325684694558107006777	29172197201340194881637647658929602533042765994956 1524809	57	187.573

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-11-19T00:49:55	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 42023 skipped known factor: 66721060831 skipped known factor: 274998859609	-	-	0.472	-	-	13.383%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-07-04T00:00:00	GrunwalderGIMP	v4_computers	?	?	42023 66721060831	51.316	16	0.010	1.39192e-5	0.022
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	274998859609	38.0006	12	8.46521e-7	1.74049e-5	2.19135e-6
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	66721060831	35.957	11	1.46415e-7	2.04548e-5	4.45436e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.303 GHz-days
Estimated T-Level:	35.436

Digits	B1	Curves	Complete	FacMiss
20	11000	2326 / 100	23.260	0.000%
25	50000	2326 / 280	8.307	0.024%
30	250000	2296 / 640	3.588	2.759%
35	1000000	1821 / 1566	1.163	31.248%
40	3000000	400 / 4588	0.087	91.650%

New Calculation Method

Total ECM effort:	18.303 GHz-days
Estimated T-Level:	35.436

Digits	B1	Complete	FacMiss
20	11000	361.169	0.000%
25	50000	75.216	0.000%
30	250000	12.281	0.000%
35	1000000	1.646	19.280%
40	3000000	0.185	83.104%
45	11000000	0.018	98.207%
50	44000000	0.002	99.844%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	0.010
250000	25000000		179	0.299
250000	25000000	378345220325684694558107006777	296	0.494
1000000	100000000		1,421	9.488
3000000	300000000		400	8.012

	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
2009-06-12T19:40:00	unconnected	dual5430	250000	25000000						30	0.050
2011-04-01T19:09:00	James Hintz	17_051310	250000	25000000						11	0.018
2014-10-09T20:41:00	James Hintz	08_04_2014	250000	25000000	378345220325684694558107006777	98.256	296	2		296	0.494
2014-10-09T22:10:00	James Hintz	08_04_2014	250000	25000000						138	0.230
2014-10-09T22:41:00	James Hintz	08_04_2014	1000000	100000000						11	0.073
2017-10-07T04:47:10	kkmrkkblmbrbk	r4.4xlarge-8	1000000	100000000						1410	9.414
2021-10-11T07:41:28	nordi	sweet16	3000000	300000000						400	8.012

Lucas-Lehmer results:
No L-L results for M21011

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:26:17

Oliver Kruse

Oliver-PC

42023

66721060831

274998859609

378345220325684694558107006777

255AB004CCAEE0DF

2017-09-21T20:26:58

Oliver Kruse

Manual testing

42023

66721060831

274998859609

378345220325684694558107006777

255AB004CCAEE0DF

2017-10-02T10:24:39

kkmrkkblmbrbk

Manual testing

42023

66721060831

274998859609

378345220325684694558107006777

255AB004CCAEE0__

2017-12-07T02:54:58

ATH

Manual testing

42023

66721060831

274998859609

378345220325684694558107006777

255AB004CCAEE0__

2020-04-17T13:49:02

Oliver Kruse

Manual testing

42023

66721060831

274998859609

378345220325684694558107006777

9233298195DF1E__

2022-05-12T18:18:40

Jorge Coveiro

Manual testing

42023

9233298195DF1E88

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)

10⁰

10¹

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10⁶

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10⁸

10⁹

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10¹

10²

10³

10⁴

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10¹⁰

10¹¹

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10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

TF factor-bounds graph:

2⁶⁷

2¹⁰

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-12T18:18:40+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