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  2. Formula for primes - Wikipedia

    en.wikipedia.org/wiki/Formula_for_primes

    In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. Formulas for calculating primes do exist; however ...

  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) All odd primes between 3 and 89, inclusive, are cluster primes. The first 10 primes that are not cluster primes are: 2, 97, 127, 149, 191, 211, 223, 227, 229, 251.

  4. 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.

  5. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. If no exponent is written then the multiplicity is 1 (since p = p 1). The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined.

  6. Prime number theorem - Wikipedia

    en.wikipedia.org/wiki/Prime_number_theorem

    The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that π c,a (x) and π c,b (x) change places when a and b are coprime to c. [34] Granville and Martin give a thorough exposition and survey. [33] Graph of the number of primes ending in 1, 3, 7, and 9 up to n ...

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  8. 40 (number) - Wikipedia

    en.wikipedia.org/wiki/40_(number)

    40 is an abundant number.. Swiss mathematician Leonhard Euler noted 40 prime numbers generated by the quadratic polynomial + +, with values =,,,...,.These forty prime numbers are the same prime numbers that are generated using the polynomial + with values of from 1 through 40, and are also known in this context as Euler's "lucky" numbers.

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