Pierpont prime

A Pierpont prime is a prime number of the form $p=1+2^{x}3^{y}$ with $-1<y\\leq x$ . If $x>0$ and $y=0$ then the resulting prime is a Fermat prime. In the Erdős-Selfridge classification of primes (http://planetmath.org/ErdHosSelfridgeClassificationOfPrimes), the Pierpont primes are class 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, etc., listed in A005109 of Sloane’s OEIS.

In 1988, Gleason showed that an $n$ -sided regular polygon can be constructed with ruler and compass if $n$ is the product of two Pierpont primes.

单词	PierpontPrime
释义	Pierpont prime A Pierpont prime is a prime number of the form $p=1+2^{x}3^{y}$ with $-1<y\\leq x$ . If $x>0$ and $y=0$ then the resulting prime is a Fermat prime. In the Erdős-Selfridge classification of primes (http://planetmath.org/ErdHosSelfridgeClassificationOfPrimes), the Pierpont primes are class 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, etc., listed in A005109 of Sloane’s OEIS. In 1988, Gleason showed that an $n$ -sided regular polygon can be constructed with ruler and compass if $n$ is the product of two Pierpont primes.
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