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  2. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    The primes of the form 2n+1 are the odd primes, including all primes other than 2. Some sequences have alternate names: 4 n +1 are Pythagorean primes, 4 n +3 are the integer Gaussian primes, and 6 n +5 are the Eisenstein primes (with 2 omitted).

  3. 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 2 2 − 1. [1] [2] The numbers p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89. [3]

  4. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    No even number greater than 2 is prime because any such number can be expressed as the product /. Therefore, every prime number other than 2 is an odd number, and is called an odd prime. [10] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all ...

  5. Largest known prime number - Wikipedia

    en.wikipedia.org/wiki/Largest_known_prime_number

    As of October 2024, the seven largest known primes are Mersenne primes. [2] The last eighteen record primes were Mersenne primes. [3] [4] The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2 k − 1 is simply k ones. [5] Finding larger prime numbers is sometimes presented as a means to stronger ...

  6. Category:Classes of prime numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Classes_of_prime...

    See List of prime numbers for definitions and examples of many classes of primes. Pages in category "Classes of prime numbers" The following 75 pages are in this category, out of 75 total.

  7. Euclid's theorem - Wikipedia

    en.wikipedia.org/wiki/Euclid's_theorem

    Since no prime number divides 1, p cannot be in the list. This means that at least one more prime number exists beyond those in the list. This proves that for every finite list of prime numbers there is a prime number not in the list. [4] In the original work, Euclid denoted the arbitrary finite set of prime numbers as A, B, Γ.

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  9. 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.