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  2. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.

  3. Minimal prime (recreational mathematics) - Wikipedia

    en.wikipedia.org/wiki/Minimal_prime...

    But it does have to be in the same order; so, for example, 991 is still a minimal prime even though a subset of the digits can form the shorter prime 19 by changing the order. Similarly, there are exactly 32 composite numbers which have no shorter composite subsequence:

  4. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    If ⁠ ⁠ really is prime, it will always answer yes, but if ⁠ ⁠ is composite then it answers yes with probability at most 1/2 and no with probability at least 1/2. [132] If this test is repeated ⁠ n {\displaystyle n} ⁠ times on the same number, the probability that a composite number could pass the test every time is at most ⁠ 1 / 2 ...

  5. List of largest known primes and probable primes - Wikipedia

    en.wikipedia.org/wiki/List_of_largest_known...

    These numbers have been proved prime by computer with a primality test for their form, for example the Lucas–Lehmer primality test for Mersenne numbers. “!” is the factorial, “#” is the primorial, and () is the third cyclotomic polynomial, defined as + +.

  6. List of Mersenne primes and perfect numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_Mersenne_primes...

    Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.

  7. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.

  8. Primality test - Wikipedia

    en.wikipedia.org/wiki/Primality_test

    A primality test is an algorithm for determining whether an input number is prime.Among other fields of mathematics, it is used for cryptography.Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not.

  9. 911 (number) - Wikipedia

    en.wikipedia.org/wiki/911_(number)

    It is a prime number, a Sophie Germain prime, and the sum of three consecutive primes (293 + 307 + 311). It is an Eisenstein prime with no imaginary part and real part of the form . Since 913 is a semiprime, 911 is a Chen prime. It is also a centered decagonal number. [1]