M4 005 453 953 Mersenne number exponent details

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is 2 ^4005453953 - 1

has 1205761787 decimal digits

takes 1,004,886.804 GHz-days to do one PRP test

0 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
Actual	2⁷¹	0.1194	54.9296%	-	-	-	-	0.1194	54.9296%
Target	2⁹²	250,402.1184	65.2174%	20000000	9600000000	197,146.2306	4.2365%	447,548.3489	66.6910%
Difference	-21	-250,401.9990	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2365%	-447,548.2296	-11.7614%

Known prime factors (4 factors, 239.8 bits, 0.00000599% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4005453953	432068317910111	15	48.618	53935 5 × 7 × 23 × 67	2012-12-18	23	67	1.326e-8	0.0092	0.0170
4005453953	861004394861697719	18	59.579	107479003 107479003	2019-12-23	1	107479003	2.661e-5	2,130.2	3,978.6
4005453953	2443091230419405481	19	61.083	304970580 2² × 3² × 5 × 1694281	2019-12-23	9	1694281	0.0001	33.583	62.718
4005453953	1683384416457089467879	22	70.512	210136533363 3³ × 81299 × 95731	2022-12-15	81299	95731	0.0857	29.861	60.189

11 Composite Factors:

P-1 results:
No P-1 results for M4005453953

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-28			2⁴⁸	2⁴⁹	432068317910111	48.618	15	3.90068e-9	236,618	8.35390e-9
2019-12-23	slaur	palvi2-rtx	2¹	2⁶⁴	2443091230419405481	61.083	19	0.001	220,968	0.002
2019-12-23	slaur	palvi2-rtx	2¹	2⁶⁴	861004394861697719	59.579	18	0.001	220,968	0.002
Missing TF 64 - 65
Missing TF 65 - 66
Missing TF 66 - 67
Missing TF 67 - 68
2022-12-15	slaur	palvi2-rtx	2⁶⁸	2⁷¹	1683384416457089467879	70.512	22	0.104	2,043,110	0.214

ECM factoring results:
No ECM results for M4005453953

Lucas-Lehmer results:
No L-L results for M4005453953

PRP results:
No PRP results for M4005453953

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

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TF factor-bounds graph:

2⁷¹

2⁶⁴

2⁴⁹

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2023-07-11T14:45:05+00:00