A180128
Maximal determinant of an n X n matrix whose elements are a permutation of the first n^2 prime numbers.
Original entry on oeis.org
1, 2, 29, 6640, 4868296, 5725998504, 11305600374272, 35954639671827328
Offset: 0
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
Cf.
A180127 [upper bounds for a(n)],
A085000 [maximal determinants for matrix elements 1, ..., n^2].
a(7) corrected, based on private communication from Richard Gosiorovsky by
Hugo Pfoertner, Aug 27 2021
A340924
8*a(n) is the maximum possible determinant of a 4 X 4 matrix whose entries are 16 consecutive primes starting with prime(n).
Original entry on oeis.org
608537, 837080, 1062261, 1335740, 1613011, 1834307, 2103606, 2369995, 2621808, 3072665, 3592140, 3891774, 4267302, 4412932, 4443915, 5039601, 5706864, 6673106, 7402050, 8535384, 9378963, 9989532, 10834096, 11530350, 11987568, 13560234, 14289963, 15119412, 15198123
Offset: 1
a(1) = 608537 = A180128(4)/8 with the corresponding matrix shown in A180128.
a(2) = 837080: determinant (
[59 19 23 7]
[11 53 37 13]
[17 5 43 41]
[29 31 3 47]) = 6696640 = 8*837080.
A340925
16*a(n) is the maximum possible determinant of a 5 X 5 matrix whose entries are 25 consecutive primes starting with prime(n).
Original entry on oeis.org
445934520, 527275650, 606375810, 668638620, 732258072, 860414368, 995563032, 1132837302, 1249798972, 1453587865, 1598993079, 1789976248, 2008319824, 2181193410, 2363922414, 2592209412, 2782039915, 3035727819, 3255326094, 3421333460, 3453338250, 3663999760, 4056944944
Offset: 2
a(2) = 445934520: determinant(
[73 53 3 79 23]
[37 101 43 5 47]
[19 41 89 71 13]
[11 31 29 61 97]
[83 7 67 17 59]) = 7134952320 = 16*445934520.
A337160
Primes p such that the 3 X 3 matrix with components (row by row) prime(k+m), 0 <= m <= 8 has zero determinant, where p = prime(k).
Original entry on oeis.org
2213, 4073, 8011, 9041, 15649, 23663, 37483, 38453, 59663, 63487, 65111, 71861, 83557, 97157, 100279, 118801, 129527, 131707, 139291, 163601, 166597, 166799, 180181, 180233, 195691, 203807, 209233, 217201, 227561, 238657, 289139, 309121, 327473
Offset: 1
The next 8 primes after 2213 are 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, and we have det({{2213, 2221, 2237}, {2239, 2243, 2251}, {2267, 2269, 2273}}) = 0, hence 2213 is a term.
-
for(k=1, 35000, M=matrix(3, 3, i, j, prime(k+3*(i-1)+j-1)); if(matdet(M, 1)==0, print1(prime(k), ", ")))
Showing 1-4 of 4 results.
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