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A Fibonacci prime is a Fibonacci number that is prime. The first few are: [46] 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many. [47] F kn is divisible by F n, so, apart from F 4 = 3, any Fibonacci prime must have a prime index.
37 is the third star number [2] and the fourth centered hexagonal number. [3]The sum of the squares of the first 37 primes is divisible by 37. [4]37 is the median value for the second prime factor of an integer.
An emirp (prime spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. [1] This definition excludes the related palindromic primes. The term reversible prime is used to mean the same as emirp, but may also, ambiguously, include the palindromic primes.
The 3-adic integers, with selected corresponding characters on their Pontryagin dual group. In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; p-adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number p ...
The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown.
If β = ω λ m + ω μ n + smaller terms, then β = (ω μ n + smaller terms)(ω λ−μ + 1)m is a product of a smaller ordinal and a prime and a natural number m. Repeating this and factorizing the natural numbers into primes gives the prime factorization of β. So the factorization of the Cantor normal form ordinal ω α 1 n 1 + ⋯ + ω α ...
In abstract algebra, a nonzero ring R is a prime ring if for any two elements a and b of R, arb = 0 for all r in R implies that either a = 0 or b = 0. This definition can be regarded as a simultaneous generalization of both integral domains and simple rings.
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (17, 19) or (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or ...
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