[1] None of the first twenty-nine natural numbers have more than two different prime factors (in other words, this is the longest such consecutive sequence; the first sphenic number or triprime, 30 is the product of the first three primes 2, 3, and 5).
29 is also, On the other hand, 29 represents the sum of the first cluster of consecutive semiprimes with distinct prime factors (14, 15).
The pair (14, 15) is also the first floor and ceiling values of imaginary parts of non-trivial zeroes in the Riemann zeta function,
Alternatively, a more precise version states that an integer quadratic matrix represents all positive integers when it contains the set of twenty-nine integers between 1 and 290:[12][13] The largest member 290 is the product between 29 and its index in the sequence of prime numbers, 10.
[16][a] The 29th dimension is the highest dimension for compact hyperbolic Coxeter polytopes that are bounded by a fundamental polyhedron, and the highest dimension that holds arithmetic discrete groups of reflections with noncompact unbounded fundamental polyhedra.