For example,    is a hoax number since  .

The first pair, triple, etc. of consecutive hoax numbers starts at 84, 12955, 291090, 9538589, 3541285143, 136063250955, and 253282144742, respectively.

Up to    there are 3183722 hoax numbers.

The smallest primitive Pythagorean triangle with 3 hoax sides is (32880, 4369, 33169).

Note that Smith numbers are defined similarly, but they take into account prime factors multiplicity. Clearly, a squarefree Smith number is also a hoax number.

The smallest 3 × 3 magic square whose entries are hoax numbers is

Below, the spiral pattern of hoax numbers up to  . See the page on prime numbers for an explanation and links to similar pictures.

The first hoax numbers are 22, 58, 84, 85, 94, 136, 160, 166, 202, 234, 250, 265, 274, 308, 319, 336, 346, 355 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many hoax numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.