M234798731 Mersenne number exponent details

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M234798731

<<<

is 2 ^234798731 - 1

has 70681461 decimal digits

takes 2,321.899 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	2⁶⁷	0.1266	58.2090%	-	-	-	-	0.1266	58.2090%	0.0000%
PrimeNet	2⁷⁵	32.5892	62.6667%	900000	55000000	55.1691	5.6895%	87.7583	64.7908%	2.1241%
GPU72	2⁷⁹	521.4389	64.5570%	1400000	55000000	61.9480	4.1848%	583.3869	66.0402%	1.4832%
Difference	-12	-521.3123	-6.3480%	-1400000	-55000000	-61.9480	-4.1848%	-583.2603	-7.8312%	-7.8312%

Known prime factors (3 factors, 168.3 bits, 0.00007169% 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
234798731	128200107127	12	36.900	273 3 × 7 × 13	2007-12-29	7	13	4.129e-11	0.0001	0.0002
234798731	18143899278778159151	20	63.976	38637132325 5² × 11 × 113 × 173 × 7187	2017-06-20	173	7187	0.0123	0.0080	0.0105
234798731	200814242247091416929	21	67.444	427630595344 2⁴ × 397 × 67322197	2022-08-05	397	67322197	0.2440	52.599	98.230

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
234798731	128200107127 18143899278778159151	2326049831240858040826055369177	31	100.876
234798731	128200107127 200814242247091416929	25744407368704448854460021352983	32	104.344
234798731	18143899278778159151 200814242247091416929	3643553385075384497473785066478857667279	40	131.421
234798731	128200107127 18143899278778159151 200814242247091416929	46710393428960777554685430639676236962575312259743 3	51	168.320

P-1 results:
No P-1 results for M234798731

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-06-20T15:12:13	TJAOI	Manual testing	2⁶³	2⁶⁴*	18143899278778159151	63.976	20	0.005	4,762	0.011
2022-08-05T09:30:49	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	200814242247091416929	67.444	21	0.117	4,762	0.241

ECM factoring results:
No ECM results for M234798731

Lucas-Lehmer results:
No L-L results for M234798731

PRP results:
No PRP results for M234798731

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁴

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-08-05T09:30:49+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