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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, ... ...

The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

A primefree sequence is sequence whose terms are never prime. Graham (1964) proved that there exist relatively prime positive integers a and b such that the recurrence ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. ...

Take K a number field and L an Abelian extension, then form a prime divisor m that is divided by all ramified primes of the extension L/K. Now define a map phi_(L/K) from the ...

An interprime is the average of consecutive (but not necessarily twin) odd primes. The first few terms are 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, ... (OEIS A024675). The first ...

A Cunningham number is a binomial number of the form C^+/-(b,n)=b^n+/-1 with b>1 and n positive integers. Bases b^k which are themselves powers need not be considered since ...

Mills (1947) proved the existence of a real constant A such that |_A^(3^n)_| (1) is prime for all integers n>=1, where |_x_| is the floor function. Mills (1947) did not, ...

A semiprime, also called a 2-almost prime, biprime (Conway et al. 2008), or pq-number, is a composite number that is the product of two (possibly equal) primes. The first few ...