AMong Neil's Challenge Sesquences, I find this one in particular fascinating: << Suggestion #6: Similar problems dealing with the spectrum of determinants: http://www.research.att.com/projects/OEIS?Anum=A089472 Sequence: 2,3,5,7,11,19,43 Name: Number of different values taken by the determinant of a real (0,1)-matrix of order n.

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To state the obvious, these are all prime. Q1: Is there any reason to think they might all be prime? ------------------------------------------------------------------------- If we allow a 0x0 matrix, then (as the empty sum) the only determinant is 0. In which case the known sequence becomes 1,2,3,5,7,11,19,43 Q2: Can it be just a coincidence that 1,2,3,7,11,19,43, (all but the fourth term, 5, of A089472) are the first 10 of the 12 "Heegner numbers" (A003173): 1,2,3,7,11,19,43,67,163 ? (As many know, 1,2,3,7,11,19,43,67,163 are the integers d > 0 for which the field Q(sqrt(-d))'s ring of algebraic integers enjoys unique factorization.) --Dan