M56842327 Mersenne number exponent details

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M56842327

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is 2 ^56842327 - 1

has 17111246 decimal digits

takes 120.474 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	1.0486	61.7647%	-	-	-	-	1.0486	61.7647%	0.0000%
PrimeNet	2⁶⁹	2.1003	62.3188%	240000	11000000	2.5392	5.4705%	4.6395	64.3802%	2.0614%
GPU72	2⁷³	33.6518	64.3836%	400000	13000000	3.3390	4.0670%	36.9907	65.8321%	1.4485%
Difference	-5	-32.6032	-2.6189%	-400000	-13000000	-3.3390	-4.0670%	-35.9421	-4.0674%	-4.0674%

Known prime factors (2 factors, 121.5 bits, 0.00021376% 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
56842327	18826400273790647	17	54.064	165601949 165601949	2000-03-08	1	165601949	6.661e-5	27.728	51.788
56842327	200368914312056174537	21	67.441	1762497463484 2² × 263 × 1831 × 915007	2022-08-03	1831	915007	0.7668	0.1585	0.2861

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
56842327	18826400273790647 200368914312056174537	3772225383263629052488796726830155439	37	121.505

P-1 results:
No P-1 results for M56842327

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-08T00:00:00	ANONYMOUS	v4_computers	?	?	18826400273790647	54.064	17	2.43904e-5	247.7	5.01441e-5
1999-12-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵³		-	-	2.11097e-5	-	-
2000-01-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵³		-	-	2.11097e-5	-	-
2022-08-10T19:29:26	LordJulius	Manual testing	2¹	2⁶⁶	18826400273790647	54.064	17	6.66097e-5	247.7	0.000
2022-08-10T19:29:26	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	0.263	-	-
2022-08-03T11:22:50	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	200368914312056174537	67.441	21	0.244	246.6	0.500
2022-08-10T19:29:26	LordJulius	Manual testing	2⁶⁷	2⁶⁸	200368914312056174537	67.441	21	0.244	246.6	0.500

ECM factoring results:
No ECM results for M56842327

Lucas-Lehmer results:
No L-L results for M56842327

PRP results:
No PRP results for M56842327

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

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁵³

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-08-10T19:29:26+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