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Given a number field K, a Galois extension field L, and prime ideals p of K and P of L unramified over p, there exists a unique element sigma=((L/K),P) of the Galois group ...

A factorial prime is a prime number of the form n!+/-1, where n! is a factorial. n!-1 is prime for n=3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, ...

A Cullen number is a number of the form C_n=2^nn+1. The first few are 3, 9, 25, 65, 161, 385, ... (OEIS A002064). Cullen numbers are divisible by p=2n-1 if p is a prime of ...

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

According to Hardy and Wright (1979), the 44-digit Ferrier's prime determined to be prime using only a mechanical calculator, is the largest prime found before the days of ...

A zerofree number n is called right truncatable if n and all numbers obtained by successively removing the rightmost digits are prime. There are exactly 83 right truncatable ...

A palindromic prime is a number that is simultaneously palindromic and prime. The first few (base-10) palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, ...

A prime magic square is a magic square consisting only of prime numbers (although the number 1 is sometimes allowed in such squares). The left square is the 3×3 prime magic ...

Let F_n be the nth Fibonacci number, and let (p|5) be a Legendre symbol so that e_p=(p/5)={1 for p=1,4 (mod 5); -1 for p=2,3 (mod 5). (1) A prime p is called a Wall-Sun-Sun ...