A Pierpont prime is a prime number of the form p = 2^k·3^l + 1. The first few Pierpont primes are 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, ... (OEIS A005109). A regular polygon of n sides can be constructed by ruler, compass and angle-trisector iff n = 2^r·3^s·p_1·p_2 ...p_k, where p_1, p_2, ..., p_k are distinct Pierpont primes and n>3. The numbers of Pierpont primes less than 10^1, 10^2, ... are 4, 10, 18, 25, 32, 42, 50, 58, ... (OEIS A113420) and the number less than 10^1, 10^2, 10^4, 10^8, ... are 4, 10, 25, 58, 125, 250, 505, 1020, 2075, 4227, ... (OEIS A113412; Caldwell).

angle trisection | compass | constructible polygon | Fermat prime | geometric construction | integer sequence primes | Proth prime | regular polygon | ruler | Sierpiński number of the second kind | Thâbit ibn Kurrah number