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  2. 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.

  3. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    A prime number (or prime) is a ... write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is reached. 2, 3, 211, 5, 23, 7 ...

  4. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...

  5. List of Mersenne primes and perfect numbers - Wikipedia

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

    For example, 3 is a Mersenne prime as it is a prime number and is expressible as 22 − 1. [ 1][ 2] The numbers p corresponding to Mersenne primes must themselves be prime, although not all primes p lead to Mersenne primes—for example, 211 − 1 = 2047 = 23 × 89. [ 3] Meanwhile, perfect numbers are natural numbers that equal the sum of their ...

  6. Sieve of Eratosthenes - Wikipedia

    en.wikipedia.org/wiki/Sieve_of_Eratosthenes

    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 ...

  7. Ulam spiral - Wikipedia

    en.wikipedia.org/wiki/Ulam_spiral

    Ulam spiral of size 201×201. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible. For comparison, a spiral with random odd numbers colored black (at the same density of primes in a 200x200 spiral). The Ulam spiral or prime spiral is a graphical depiction of the ...

  8. Prime number theorem - Wikipedia

    en.wikipedia.org/wiki/Prime_number_theorem

    The prime number theorem is obtained there in an equivalent form that the Cesaro sum of the values of the Liouville function is zero. The Liouville function is () where () is the number of prime factors, with multiplicity, of the integer .

  9. Mersenne prime - Wikipedia

    en.wikipedia.org/wiki/Mersenne_prime

    Mersenne primes (of form 2^ p − 1 where p is a prime) In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.

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