M3 975 740 081 Mersenne number exponent details

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is 2 ^3975740081 - 1

has 1196817020 decimal digits

takes 997,432.199 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	2⁶⁴	0.0009	50.0000%	-	-	-	-	0.0009	50.0000%
Target	2⁹²	252,273.5728	65.2174%	20000000	9600000000	197,146.2306	4.2335%	449,419.8034	66.6899%
Difference	-28	-252,273.5719	-15.2174%	-20000000	-9600000000	-197,146.2306	-4.2335%	-449,419.8025	-16.6899%

Known prime factors (3 factors, 165.3 bits, 0.00000416% 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
3975740081	286253285833	12	38.059	36 2² × 3²	2012-08-20	9	9	1.000e-11	0.0033	0.0067
3975740081	146392633877739881	18	57.023	18410740 2² × 5 × 131 × 7027	2019-12-22	131	7027	5.289e-6	0.1843	0.2600
3975740081	1372384680979695140783	22	70.217	172594869511 17 × 37 × 6961 × 39419	2023-07-22	6961	39419	0.0903	3.1755	5.1535

4 Composite Factors:

P-1 results:
No P-1 results for M3975740081

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-12-22	slaur	palvi2-rtx	2¹	2⁶⁴	146392633877739881	57.023	18	0.001	219,328	0.002
Missing TF 64 - 65
Missing TF 65 - 66
Missing TF 66 - 67
Missing TF 67 - 68
2023-07-22	slaur	palvi2-rtx	2⁶⁸	2⁷¹	1372384680979695140783	70.217	22	0.105	2,025,530	0.240

ECM factoring results:
No ECM results for M3975740081

Lucas-Lehmer results:
No L-L results for M3975740081

PRP results:
No PRP results for M3975740081

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

10⁰

10¹

10²

10³

10⁴

10⁰

10¹

10²

10³

10⁴

10⁵

TF factor-bounds graph:

2⁷¹

2⁶⁴

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2023-07-22T15:17:02+00:00