A Pierpont prime is a prime number of the form . 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).
where ,
, ..., are distinct Pierpont primes and (Gleason 1998).
The numbers of Pierpont primes less than , , ... are 4, 10, 18, 25, 32, 42, 50, 58, ... (OEIS A113420)
and the number less than ,
, , , ... are 4, 10, 25, 58, 125, 250, 505, 1020, 2075, 4227,
... (OEIS A113412; Caldwell).
Caldwell, C. "Pierpont primes." primeform posting, Oct. 25, 2005. http://groups.yahoo.com/group/primeform/message/6588/.Cox,
D. A. and Shurman, J. "Geometry and Number Theory on Clovers." Amer.
Math. Monthly112, 682-704, 2005.Gleason, A. M. "Angle
Trisection, the Heptagon, and the Triskaidecagon." Amer. Math. Monthly95,
185-194, 1988.Guy, R. K. §A18 in Unsolved
Problems in Number Theory, 3rd ed. New York: Springer-Verlag, 2004.Martin,
G. E Geometric
Constructions. New York: Springer, 1998.Pierpont, J. "On
an Undemonstrated Theorem of the Disquisitiones Arithmeticae." Bull. Amer.
Math. Soc.2, 77-83, 1895-1896.Sloane, N. J. A.
Sequences A005109/M0673, A113412,
and A113420 in "The On-Line Encyclopedia
of Integer Sequences."
. 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).
sides can be constructed by ruler,
compass and angle-trisector iff
,
, ..., 
are distinct Pierpont primes and 
(Gleason 1998).
, 
, ... are 4, 10, 18, 25, 32, 42, 50, 58, ... (OEIS A113420)
and the number less than 
,
, 
, 
, ... are 4, 10, 25, 58, 125, 250, 505, 1020, 2075, 4227,
... (OEIS A113412; Caldwell).
, which has 
decimal digits (http://primes.utm.edu/primes/page.php?id=87449).
