M427962001 Mersenne number exponent details

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M427962001

<<<

is 2 ^427962001 - 1

has 128829400 decimal digits

takes 9,022.866 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	2⁶⁸	0.1393	57.3529%	-	-	-	-	0.1393	57.3529%	0.0000%
PrimeNet	2⁷⁸	143.0419	62.8205%	1600000	110000000	229.4626	5.5688%	372.5045	64.8909%	2.0704%
GPU72	2⁸²	2,288.6770	64.6341%	2400000	110000000	252.5868	4.1250%	2,541.2637	66.0930%	1.4589%
Difference	-14	-2,288.5377	-7.2812%	-2400000	-110000000	-252.5868	-4.1250%	-2,541.1245	-8.7401%	-8.7401%

Known prime factors (3 factors, 177.3 bits, 0.00004142% 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
427962001	10376759545362919	17	53.204	12123459 3³ × 277 × 1621	2008-03-08	277	1621	3.155e-6	0.0107	0.0172
427962001	110074992720083399	18	56.611	128603699 7 × 18371957	2015-04-16	7	18371957	2.913e-5	30.600	57.152
427962001	200780933559383915687	21	67.444	234577991843 13 × 19 × 949708469	2022-08-05	19	949708469	0.0770	1,581.8	2,954.4

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
427962001	10376759545362919 110074992720083399	1142221731413879230052273402081681	34	109.815
427962001	10376759545362919 200780933559383915687	2083455468839215087050990533712210353	37	120.648
427962001	110074992720083399 200780933559383915687	22100959799880733136009537857824380113	38	124.055
427962001	10376759545362919 110074992720083399 200780933559383915687	22933634556509454566029767096620543474110469479122 9847	54	177.260

P-1 results:
No P-1 results for M427962001

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-04-16T11:44:00	TJAOI	Manual testing	2⁵⁶	2⁵⁷*	110074992720083399	56.611	18	6.69515e-6	18,509	1.37338e-5
2022-08-05T09:29:47	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	200780933559383915687	67.444	21	0.008	18,509	0.016
2022-08-10T19:29:46	LordJulius	Manual testing	2¹	2⁶⁸	10376759545362919	53.204	17	3.15519e-6	18,509	6.47227e-6
2022-08-10T19:29:46	LordJulius	Manual testing	2¹	2⁶⁸	200780933559383915687	67.444	21	0.077	18,509	0.158
2022-08-10T19:29:47	LordJulius	Manual testing	2¹	2⁶⁸	110074992720083399	56.611	18	2.91256e-5	18,509	5.97456e-5

ECM factoring results:
No ECM results for M427962001

Lucas-Lehmer results:
No L-L results for M427962001

PRP results:
No PRP results for M427962001

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

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10³

10⁰

10¹

10²

10³

10⁴

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10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-08-10T19:29:47+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