M1458151 Mersenne number exponent details

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M1458151

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>>>

is 2 ^1458151 - 1

has 438948 decimal digits

takes 0.056 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	ABC70B9105CD3E23	double-checked
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	20.3778	68.6567%	2000000	60000000	0.2857	7.2332%	20.6635	70.9238%	2.2671%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9073%	0.0073	63.5902%	1.0902%
GPU72	2⁶⁰	0.1053	65.0000%	6500	90000	0.0006	1.3982%	0.1059	65.4894%	0.4894%
Difference	+7	+20.2725	+3.6567%	+1993500	+59910000	+0.2851	+5.8350%	+20.5575	+5.4345%	+5.4345%

Known prime factors (1 factor, 71.9 bits, 0.00493122% 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
1458151	4420293365933249145353	22	71.905	1515718662173276 2² × 11 × 43 × 801119800303	2015-05-14	43	801119800303	340.36	2,416.4	4,513.1

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.840%
2010-09-17T13:24:00	Rob_Dee	twopc	100000	200000		-		-	-	0.006	-	-	1.217%
2010-09-18T11:27:00	Rob_Dee	twopc	200000	300000		-		-	-	0.011	-	-	1.521%
2010-09-19T11:34:00	Rob_Dee	twopc	200000	1000000		-		-	-	0.013	-	-	2.335%
2010-09-20T12:05:00	Rob_Dee	twopc	200000	2000000		-		-	-	0.017	-	-	2.822%
2010-09-21T12:14:00	Rob_Dee	twopc	200000	3000000		-		-	-	0.020	-	-	3.113%
2010-09-22T13:37:00	Rob_Dee	twopc	200000	4000000		-		-	-	0.023	-	-	3.323%
2010-09-23T12:02:00	Rob_Dee	twopc	200000	5000000		-		-	-	0.026	-	-	3.487%
2014-11-19T23:20:00	Jocelyn Larouche	Manual testing	244017	244017		-		-	-	0.014	-	-	1.387%
2015-01-26T12:23:00	Jocelyn Larouche	Manual testing	295259	295259		-		-	-	0.016	-	-	1.520%
2015-01-28T11:16:00	Jocelyn Larouche	Manual testing	324784	324784		-		-	-	0.018	-	-	1.590%
2015-01-31T14:55:00	Jocelyn Larouche	Manual testing	357262	357262		-		-	-	0.020	-	-	1.661%
2015-02-14T12:30:00	Jocelyn Larouche	Manual testing	392988	392988		-		-	-	0.022	-	-	1.735%
2015-02-16T12:52:00	alpertron	Manual testing	2000000	60000000		-		-	-	0.286	-	-	7.233%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2010-05-09T04:20:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.105	-	-
2011-04-05T20:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.095	-	-
2015-03-28T21:58:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.346	-	-
2015-03-28T21:58:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.562	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.558 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.558 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	11.80
50000	5000000	4420293365933249145353	2	0.095
250000	35000000		50	13.66

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-06T04:43:00	Sturle Sunde	minister	50000	5000000						1	0.047
2009-01-01T23:30:00	Martti Järvi	SKYNET	50000	5000000						3	0.142
2009-09-28T01:48:00	JimBa	NASsrvr	50000	5000000						3	0.142
2010-04-22T17:08:00	unconnected	X3220--xp	50000	5000000						3	0.142
2011-07-25T01:43:00	Beat Bucheli	I7	50000	5000000						3	0.142
2012-11-24T04:34:00	Donna Noble	PH2x6	50000	5000000						3	0.142
2013-09-07T10:10:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2014-02-17T13:47:00	Bruce	snowflake	50000	5000000						3	0.142
2014-11-12T05:07:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-05-14T08:11:00	Chang Chia-Tche	exbpc13	50000	5000000	4420293365933249145353	71.905	2	2		2	0.095
2019-03-22T12:42:47	TJAOI	Manual testing	50000	5000000						224	10.61
2021-12-28T11:13:11	TJAOI	Manual testing	250000	35000000						50	13.66

Lucas-Lehmer results:
No L-L results for M1458151

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T02:54:20

Oliver Kruse

GTX-3

4420293365933249145353

6FF005BD85C8CF__

2017-10-27T18:25:29

kkmrkkblmbrbk

c4.xlarge

4420293365933249145353

6FF005BD85C8CF__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 200000, B2 = 4000000 (P-1 stage 2)

B1 = 392988 (P-1 stage 1)

B1 = 357262 (P-1 stage 1)

B1 = 200000, B2 = 3000000 (P-1 stage 2)

B1 = 324784 (P-1 stage 1)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 295259 (P-1 stage 1)

B1 = 244017 (P-1 stage 1)

B1 = 200000, B2 = 1000000 (P-1 stage 2)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

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10⁰

10¹

10²

10³

10⁴

10⁵

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TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶¹

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-12-28T11:13:11+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