M21221 Mersenne number exponent details

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M21221

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>>>

is 2 ²¹²²¹ - 1

has 6389 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	1,400.2129	77.6119%	500000000	10000000000	0.4722	13.3915%	1,400.6850	80.6100%	2.9981%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	3.7538%	0.0000	63.9077%	1.4077%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.5872%	0.0001	66.4502%	0.5411%
Difference	+23	+1,400.2128	+11.7028%	+499999500	+9999990000	+0.4722	+11.8042%	+1,400.6849	+14.1598%	+14.1598%

Known prime factors (4 factors, 195.3 bits, 0.92023791% 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
21221	636631	6	19.280	15 3 × 5	-	3	5	3.302e-12	1.443e-9	2.833e-9
21221	2546521	7	21.280	60 2² × 3 × 5	2008-08-26	4	5	1.334e-11	1.881e-9	3.777e-9
21221	694855970094079	15	49.304	16371895059 3² × 13 × 9397 × 14891	2008-08-26	9397	14891	0.0043	4.499e-6	8.874e-6
21221	54264694995610323463578429783479	32	105.420	1278561212846009223495085759 107 × 241 × 17921 × 2766677034942919117	2021-10-19	17921	2766677034942919117	6.376e+12	69,941,595	130,631,423

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
21221	636631 2546521	1621194210751	13	40.560
21221	636631 694855970094079	442366851096963607849	21	68.584
21221	2546521 694855970094079	1769465319819944149159	22	70.584
21221	636631 2546521 694855970094079	1126496476022290863623243329	28	89.864
21221	636631 54264694995610323463578429783479	34546587039750395836941399331486019249	38	124.700
21221	2546521 54264694995610323463578429783479	138186185364916596516795206590654726559	39	126.700
21221	636631 2546521 54264694995610323463578429783479	87973609375052217757083849167015109223982729	44	145.980
21221	694855970094079 54264694995610323463578429783479	37706147283034125292790573119406185615229920841	47	154.723
21221	636631 694855970094079 54264694995610323463578429783479	24004902250945298219274555355580679354409439734926 671	53	174.004
21221	2546521 694855970094079 54264694995610323463578429783479	96019495885339343774722343050603359199080913249944 161	53	176.004
21221	636631 2546521 694855970094079 54264694995610323463578429783479	61128987684979471766645259978648667170270080883225 201161591	59	195.284

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: 636631 skipped known factor: 2546521 skipped known factor: 694855970094079	-	-	0.472	-	-	13.391%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	2546521	21.280	7	1.70977e-13	2.09559e-5	5.27628e-13
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	694855970094079	49.304	15	0.001	1.40536e-5	0.002

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.303 GHz-days
Estimated T-Level:	35.426

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 / 1580	1.153	31.572%
40	3000000	400 / 4700	0.085	91.841%

New Calculation Method

Total ECM effort:	18.303 GHz-days
Estimated T-Level:	35.426

Digits	B1	Complete	FacMiss
20	11000	323.551	0.000%
25	50000	65.458	0.000%
30	250000	10.642	0.002%
35	1000000	1.404	24.560%
40	3000000	0.155	85.626%
45	11000000	0.015	98.511%
50	44000000	0.001	99.871%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	0.010
250000	25000000		475	0.793
1000000	100000000		1,421	9.488
3000000	300000000		367	7.351
3000000	300000000	54264694995610323463578429783479	33	0.661

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-02T14:40:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.010
2009-06-13T06:05:00	unconnected	dual5430	250000	25000000						30	0.050
2011-03-29T07:33:00	James Hintz	17_051310	250000	25000000						11	0.018
2014-10-10T17:18:00	James Hintz	08_04_2014	250000	25000000						434	0.724
2014-10-10T17:36:00	James Hintz	08_04_2014	1000000	100000000						11	0.073
2017-10-22T23:33:00	kkmrkkblmbrbk	r4.xlarge	1000000	100000000						1410	9.414
2021-10-19T02:30:44	nordi	sweet16	3000000	300000000	54264694995610323463578429783479	105.420	33	2	5413391649756996	33	0.661
2021-10-21T07:19:59	nordi	sweet16	3000000	300000000						367	7.351

Lucas-Lehmer results:
No L-L results for M21221

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:26:45

Oliver Kruse

PRP

636631

2546521

694855970094079

2132A74E6208B0__

2017-09-21T20:26:59

Oliver Kruse

Manual testing

636631

2546521

694855970094079

2132A74E6208B0__

2017-10-12T16:29:44

kkmrkkblmbrbk

Manual testing

636631

2546521

694855970094079

2132A74E6208B0__

2020-04-17T13:49:05

Oliver Kruse

Manual testing

636631

2546521

694855970094079

C4376C53C4D873__

2021-10-19T03:05:43

H Michaelson

636631

2546521

694855970094079

54264694995610323463578429783479

C4376C53C4D873EE

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

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TF factor-bounds graph:

2⁶⁷

2¹⁰

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2021-10-21T07:19:59+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