The sequence of currently known Sierpiński numbers begins with:78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, 965431, … (sequence A076336 in OEIS).The number 78557 wa ...
It has been conjectured that there are infinitely many Wall–Sun–Sun primes. No Wall–Sun–Sun primes are known as of March 2014.In 2007, Richard J. McIntosh and Eric L. Roettger showed that if any e ...
Wolstenholme prime can be defined in a number of equivalent ways.Definition via binomial coefficients A Wolstenholme prime is a prime number p 7 that satisfies the congruence{2p-1 \choose p-1} \equiv ...
Near-Wilson primes A prime p satisfying the congruence (p ? 1)! ≡ ? 1 + Bp (mod p2) with small |B| can be called a near-Wilson prime. Near-Wilson primes with B = 0 represent Wilson primes. The foll ...
The stronger version of Fermat's little theorem, which a Wieferich prime satisfies, is usually expressed as a congruence relation 2p ? 1 ≡ 1 (mod p2). From the definition of the congruence relation ...
The positive integer n is square-free if and only if in the prime factorization of n, no prime number occurs more than once. Another way of stating the same is that for every prime factor p of n, the ...
Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether the set of Mersenne primes is finite or infinite. The Lenstra–Pomerance–Wagstaff conjecture asserts t ...
It is not known whether there are infinitely many Fibonacci primes. The first 33 are Fn for the n values (sequence A001605 in OEIS):3, 4, 5, 7, 11, 13, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, ...
A palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while pri ...
In number theory, a Woodall number (Wn) is any natural number of the formW_n = n \times 2^n - 1for some natural number n. The first few Woodall numbers are:1, 7, 23, 63, 159, 383, 895, … (sequence A0 ...
In mathematics, a Cullen number is a natural number of the form n \cdot 2^n + 1 (written C_n). Cullen numbers were first studied by Fr. James Cullen in 1905. Cullen numbers are special cases of Proth ...
Class number criterion An odd prime number p is defined to be regular if it does not divide the class number of the p-th cyclotomic field Q(ζp), where ζp is a p-th root of unity. The prime number 2 ...
In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 29 is a Sophie Germa ...
The first three Wagstaff primes are 3, 11, and 43 because\begin{align}3 = {2^3+1 \over 3}, \\11 = {2^5+1 \over 3}, \\43 = {2^7+1 \over 3}.\end{align}Known Wagstaff primes The first few Wagstaff pri ...
