M1438207 Mersenne number exponent details

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is 2 ^1438207 - 1

has 432944 decimal digits

takes 0.055 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	F73963D8EDEBFCE3	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	20.6604	68.6567%	2000000	60000000	0.2857	7.2228%	20.9461	70.9206%	2.2639%
PrimeNet	2⁵⁶	0.0067	62.5000%	6500	110000	0.0007	2.7766%	0.0073	63.5412%	1.0412%
GPU72	2⁶⁰	0.1068	65.0000%	6000	90000	0.0006	1.3547%	0.1074	65.4742%	0.4742%
Difference	+7	+20.5536	+3.6567%	+1994000	+59910000	+0.2851	+5.8681%	+20.8387	+5.4464%	+5.4464%

Known prime factors (1 factor, 77.1 bits, 0.00535966% 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
1438207	160058347514958805401737	24	77.083	55645100988577724 2² × 13 × 408389 × 2620291183	2015-04-25	408389	2620291183	38,345	7.9249	14.762

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	-	-	0.837%
2009-08-14T06:20:00	markr	lounge	200000	5000000		-		-	-	0.026	-	-	3.481%
2014-11-14T01:20:00	Jocelyn Larouche	Manual testing	244628	244628		-		-	-	0.014	-	-	1.385%
2015-01-27T21:58:00	Jocelyn Larouche	Manual testing	325598	325598		-		-	-	0.018	-	-	1.588%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	358157	358157		-		-	-	0.020	-	-	1.660%
2015-02-13T17:59:00	Jocelyn Larouche	Manual testing	393972	393972		-		-	-	0.022	-	-	1.733%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	476705	476705		-		-	-	0.026	-	-	1.885%
2015-03-03T20:46:00	Jocelyn Larouche	Manual testing	524375	524375		-		-	-	0.029	-	-	1.964%
2015-03-10T07:55:00	Jocelyn Larouche	Manual testing	576812	576812		-		-	-	0.032	-	-	2.044%
2015-04-08T16:58:00	Jocelyn Larouche	Manual testing	767736	767736		-		-	-	0.043	-	-	2.297%
unknown			2000000	60000000		-		-	-	0.286	-	-	7.223%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.007	-	-
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-
2010-05-11T03:20:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.107	-	-
2011-05-07T23:53:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.110	-	-
2015-03-22T03:57:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.365	-	-
2015-03-22T03:57:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.598	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.492 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:	25.492 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		250	11.82
50000	5000000	160058347514958805401737	1	0.047
250000	35000000		50	13.63

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	F73963D8EDEBFCE3	0.055

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:22

alpertron

Manual testing

160058347514958805401737

11254A7B654CF1__

no

2017-10-18T06:53:50

Oliver Kruse

GTX-2

160058347514958805401737

11254A7B654CF1__

no

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 = 767736 (P-1 stage 1)

B1 = 576812 (P-1 stage 1)

B1 = 524375 (P-1 stage 1)

B1 = 476705 (P-1 stage 1)

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

B1 = 393972 (P-1 stage 1)

B1 = 358157 (P-1 stage 1)

B1 = 325598 (P-1 stage 1)

B1 = 244628 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-10-28T13:38:35+00:00