A Pierpont prime is a prime number of the form , where and are nonnegative integers.
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 ,, and are nonnegative integers
and ,, ..., are distinct Pierpont primes greater than 3 (Gleason 1988).
The numbers of Pierpont primes less than ,, ... are 4, 10, 18, 25, 32, 42, 50, 58, ... (OEIS
A113420) and the numbers less than ,,,, ... are 4, 10, 25, 58, 125,
250, 505, 1020, 2075, 4227, ... (OEIS A113412;
Caldwell).
As of Oct. 2026, the largest known Pierpont prime is , which has 6,170,560 decimal
digits and was reported by R. Propper in Jun. 2023 (PrimePages 2023).
Caldwell, C. "Pierpont primes." primeform posting, Oct. 25, 2005. https://oeis.org/A113432/a113432.pdf.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.PrimePages. "." 2023. https://t5k.org/primes/page.php?id=136165.Sloane,
N. J. A. Sequences A005109/M0673,
A113412, and A113420
in "The On-Line Encyclopedia of Integer Sequences."
, where 
and 
are nonnegative integers.
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
, 
, and 
are nonnegative integers
and 
, 
, ..., 
are distinct Pierpont primes greater than 3 (Gleason 1988).
, 
, ... are 4, 10, 18, 25, 32, 42, 50, 58, ... (OEIS
A113420) and the numbers less than 
, 
, 
, 
, ... are 4, 10, 25, 58, 125,
250, 505, 1020, 2075, 4227, ... (OEIS A113412;
Caldwell).
, which has 6,170,560 decimal
digits and was reported by R. Propper in Jun. 2023 (PrimePages 2023).
." 2023.