M1866211 Mersenne number exponent details

≡

M1866211

<<<

>>>

is 2 ^1866211 - 1

has 561786 decimal digits

takes 0.101 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	15.9221	68.6567%	500000	15000000	0.1015	5.0806%	16.0235	70.2491%	1.5924%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0280%	0.0116	64.2735%	1.1156%
GPU72	2⁶¹	0.1646	65.5738%	10000	150000	0.0014	1.6889%	0.1660	66.1552%	0.5814%
Difference	+6	+15.7575	+3.0829%	+490000	+14850000	+0.1001	+3.3916%	+15.8575	+4.0939%	+4.0939%

Known prime factors (4 factors, 170.6 bits, 0.00914260% 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
1866211	134367193	9	27.002	36 2² × 3²	-	9	9	9.656e-12	7.080e-7	1.441e-6
1866211	13858482887	11	33.690	3713 47 × 79	2008-07-15	47	79	1.106e-9	3.834e-6	7.524e-6
1866211	307331359903	12	38.161	82341 3² × 7 × 1307	2008-07-15	9	1307	3.577e-8	6.271e-6	1.044e-5
1866211	4019393588667457879009	22	71.767	1076886158282064 2⁴ × 3² × 13² × 151 × 293051299	2020-10-12	169	293051299	357.35	1.2560	2.3458

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1866211	134367193 13858482887	1862125444764726191	19	60.692
1866211	134367193 307331359903	41295252151038862279	20	65.163
1866211	13858482887 307331359903	4259146391854163479961	22	71.851
1866211	134367193 4019393588667457879009	540074634071442925648172951737	30	98.769
1866211	134367193 13858482887 307331359903	572289545249522012165471319473	30	98.853
1866211	13858482887 4019393588667457879009	55702697264665482150039543018983	32	105.458
1866211	307331359903 4019393588667457879009	1235285697590569239597808007976127	34	109.928
1866211	134367193 13858482887 4019393588667457879009	7484615073981878920492418234463491424719	40	132.459
1866211	134367193 307331359903 4019393588667457879009	165981871738291651996901910984673796001511	42	136.930
1866211	13858482887 307331359903 4019393588667457879009	17119185700614760939554825041248715534038649	44	143.619
1866211	134367193 13858482887 307331359903 4019393588667457879009	23002569290373438018140245103986991211642692196422 57	52	170.620

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:37:32	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 134367193 skipped known factor: 13858482887 skipped known factor: 307331359903	-	-	0.101	-	-	5.081%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	13858482887	33.690	11	4.92806e-10	0.216	1.05232e-9
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	307331359903	38.161	12	1.61435e-8	0.216	3.44722e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.818 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	19.818 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.798	0.015%
25	50000	0.798	45.041%
30	250000	0.049	95.185%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		26	1.800
50000	5000000	4019393588667457879009	3	0.208
50000	6600000		214	16.71
50000	6750000		14	1.105

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T14:08:51	Oliver Kruse	O2.261	50000	5000000						3	0.208
2019-01-19T04:15:16	tottenhoff	i7-8700k-01	50000	5000000						3	0.208
2020-07-05T04:04:43	argusdusty	Argus-PC	50000	5000000						3	0.208
2020-07-13T17:35:44	argusdusty	Manual testing	50000	5000000						3	0.208
2020-10-12T13:09:34	nordi	sweet16	50000	5000000	4019393588667457879009	71.767	3	2	2579762622005065	3	0.208
2020-11-01T10:11:45	nordi	sweet16	50000	5000000						7	0.485
2021-01-23T10:46:40	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.485
2021-05-01T15:41:12	nordi	sweet16	50000	6750000						7	0.552
2021-08-16T17:21:54	nordi	sweet16	50000	6750000						7	0.552
2021-08-27T10:08:41	TJAOI	Manual testing	50000	6600000						214	16.71

Lucas-Lehmer results:
No L-L results for M1866211

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T10:17:30

Oliver Kruse

GTX-3

134367193

13858482887

307331359903

58DAEB97538AEC__

2017-11-07T16:02:38

Chang Chia-Tche

exbpc13

134367193

13858482887

307331359903

58DAEB97538AEC__

2020-10-12T15:56:57

mrh.org

134367193

13858482887

307331359903

4019393588667457879009

F6D76C550FB68FE7

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

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-08-27T10:08:41+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