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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 cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , ... ( OEIS : A038134 )

  4. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of 5 ...

  5. Prime omega function - Wikipedia

    en.wikipedia.org/wiki/Prime_omega_function

    In number theory, the prime omega functions and () count the number of prime factors of a natural number . Thereby ω ( n ) {\displaystyle \omega (n)} (little omega) counts each distinct prime factor, whereas the related function Ω ( n ) {\displaystyle \Omega (n)} (big omega) counts the total number of prime factors of n , {\displaystyle n ...

  6. Category:Prime numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Prime_numbers

    This category includes articles relating to prime numbers and primality. For a list of prime numbers, see list of prime numbers . This category roughly corresponds to MSC 11A41 Primes and MSC 11A51 Factorization; primality

  7. List of Mersenne primes and perfect numbers - Wikipedia

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

    However, in this case, there is some fortuitous cancellation between the two factors of P n modulo 25, resulting in P 4k −1 ≡ 3 (mod 25). Combined with the fact that P 4 k −1 is a multiple of 8 whenever k > 1 , we have P 4 k −1 ≡ 128 (mod 200) and ends in 128, 328, 528, 728 or 928.

  8. Euclid's lemma - Wikipedia

    en.wikipedia.org/wiki/Euclid's_lemma

    Any prime number is prime to any number it does not measure. [note 6] Proposition 30 If two numbers, by multiplying one another, make the same number, and any prime number measures the product, it also measures one of the original numbers. [note 7] Proof of 30 If c, a prime number, measure ab, c measures either a or b. Suppose c does not measure a.

  9. Safe and Sophie Germain primes - Wikipedia

    en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes

    A prime number q is a strong prime if q + 1 and q − 1 both have some large (around 500 digits) prime factors. For a safe prime q = 2p + 1, the number q − 1 naturally has a large prime factor, namely p, and so a safe prime q meets part of the criteria for being a strong prime. The running times of some methods of factoring a number with q as ...

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