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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. 225 (number) - Wikipedia

    en.wikipedia.org/wiki/225_(number)

    After 1 and 9, 225 is the third smallest number n for which σ(φ(n)) = φ(σ(n)), where σ is the sum of divisors function and φ is Euler's totient function. [8] 225 is a refactorable number. [9] 225 is the smallest square number to have one of every digit in some number base (225 is 3201 in base 4) [10] 225 is the first odd number with ...

  4. 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.

  5. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    The progressions of numbers that are 0, 3, or 6 mod 9 contain at most one prime number (the number 3); the remaining progressions of numbers that are 2, 4, 5, 7, and 8 mod 9 have infinitely many prime numbers, with similar numbers of primes in each progression.

  6. 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, ... 225 9693×2 7767343 − 1 17 November 2023 2,338,208 226 5×2 7755002 − 1

  7. List of numbers - Wikipedia, the free encyclopedia

    en.wikipedia.org/wiki/List_of_numbers

    A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.

  8. 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]

  9. 229 (number) - Wikipedia

    en.wikipedia.org/wiki/229_(number)

    It is the fiftieth prime number, and a regular prime. [1] It is also a full reptend prime, meaning that the decimal expansion of the unit fraction 1/229 repeats periodically with as long a period as possible. [2] With 227 it is the larger of a pair of twin primes, [3] and it is also the start of a sequence of three consecutive squarefree ...