Maximiliano Lucius

Boundary Certificates and an Information Barrier for a Six-Direction Affine Plank Problem on a Triangle

Bang's affine plank conjecture asserts that any collection of planks covering a convex body K in R^d has total relative width at least 1. The conjecture remains open, including in the plane, where the best known dimension-wide lower bound is 2/(1+sqrt(d)). This paper does not add...

Boundary Certificates and an Information Barrier for a Six-Direction Affine Plank Problem on a Triangle

Bang's affine plank conjecture asserts that any collection of planks covering a convex body K in R^d has total relative width at least 1. The conjecture remains open, including in the plane, where the best known dimension-wide lower bound is 2/(1+sqrt(d)). This paper does not add...

The Product-Index Prime Conjecture: Corrected Reductions and Requirements for a Complete Computation

Let p_n denote the nth prime and let D(m) be the product of the decimal digits of m. A product-index prime is a prime p_n satisfying D(p_n) = n. The known examples are p_7 = 17, p_21 = 73, and p_181440 = 2475989, and it has been conjectured that these are the only examples. This...

The Product-Index Prime Conjecture: Corrected Reductions and Requirements for a Complete Computation

Let p_n denote the nth prime and let D(m) be the product of the decimal digits of m. A product-index prime is a prime p_n satisfying D(p_n) = n. The known examples are p_7 = 17, p_21 = 73, and p_181440 = 2475989, and it has been conjectured that these are the only examples. This...