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A180128
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Maximal determinant of an n X n matrix whose elements are a permutation of the first n^2 prime numbers.
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10
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OFFSET
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0,2
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COMMENTS
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The terms a(5), a(6), a(7) were found by tabu search, with strong numerical evidence for the optimality of a(7).
A known lower bound for the next term a(8) is 154665569137423060000.
Upper bounds for higher terms can be found by the method described by O. Gasper, H. Pfoertner and M. Sigg, and are given in A180127, e.g., a(8) <= 154715716383037989022.
An improved lower bound is a(8) >= 154671943501236284416, provided in a private communication by Richard Gosiorovsky. - Hugo Pfoertner, Aug 27 2021
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LINKS
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EXAMPLE
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a(2) = 29:
. 7 3
. 2 5
a(3) = 6640:
. 23 11 5
. 3 17 13
. 7 2 19
a(4) = 4868296:
. 53 11 23 13
. 17 47 29 3
. 7 5 43 37
. 19 31 2 41
a(5) = 5725998504
. 89 41 23 2 53
. 31 97 29 47 11
. 59 13 79 61 7
. 37 19 5 83 67
. 3 43 71 17 73
a(6) = 11305600374272:
. 137 73 7 89 83 13
. 79 139 67 19 3 97
. 101 5 149 61 37 53
. 2 109 103 71 113 11
. 59 29 41 17 131 127
. 23 47 43 151 31 107
a(7) = 35954639671827332:
. 227 71 173 43 83 29 73
. 151 163 5 181 2 103 89
. 31 223 139 61 137 97 13
. 23 47 157 211 109 19 131
. 113 7 67 127 167 199 17
. 53 79 149 37 11 193 179
. 101 107 3 41 191 59 197
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CROSSREFS
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Cf. A180127 [upper bounds for a(n)], A085000 [maximal determinants for matrix elements 1, ..., n^2].
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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a(7) corrected, based on private communication from Richard Gosiorovsky by Hugo Pfoertner, Aug 27 2021
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STATUS
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approved
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