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).

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

Author

Hugo Pfoertner, Jan 26 2021

Keywords

• nonn

Comments

The entries of the matrix are arranged in such a way that the determinant of the matrix is maximized.

The special case of the first matrix with determinant A180128(5) = 5725998504 is excluded, since the prime number 2 prevents the otherwise existing divisibility of the determinant by 16.

Examples

			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.
		

Crossrefs

Cf. A118815, A180128, A340923, A340924.