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An illegal prime is an illegal number which is also prime.One of the earliest illegal prime numbers was generated in March 2001 by Phil Carmody.Its binary representation corresponds to a compressed version of the C source code of a computer program implementing the DeCSS decryption algorithm, which can be used by a computer to circumvent a DVD's copy protection.
The first deterministic primality test significantly faster than the naive methods was the cyclotomy test; its runtime can be proven to be O((log n) c log log log n), where n is the number to test for primality and c is a constant independent of n. Many further improvements were made, but none could be proven to have polynomial running time.
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that ...
All prime numbers from 37 to 133,916,180,167,633 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random prime in same range. Prime Numbers List Full list for prime numbers below 10,000,000,000, partial list for up to 400 digits.
The following is pseudocode which combines Atkin's algorithms 3.1, 3.2, and 3.3 by using a combined set "s" of all the numbers modulo 60 excluding those which are multiples of the prime numbers 2, 3, and 5, as per the algorithms, for a straightforward version of the algorithm that supports optional bit packing of the wheel; although not specifically mentioned in the referenced paper, this ...
AKS is the first primality-proving algorithm to be simultaneously general, polynomial-time, deterministic, and unconditionally correct. Previous algorithms had been developed for centuries and achieved three of these properties at most, but not all four. The AKS algorithm can be used to verify the primality of any general number given.
Sexy prime. Solinas prime. Sophie Germain prime. Safe and Sophie Germain primes. Stern prime. Strobogrammatic number. Strong prime. Super-prime. Supersingular prime (algebraic number theory)
In number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example is the sequence of primes (3, 7, 11), which is given by for . According to the Green–Tao theorem, there exist arbitrarily long arithmetic progressions in the sequence of primes.