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  2. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    It follows that arbitrarily large prime numbers can be found as the prime factors of the numbers !, leading to a proof of Euclid's theorem that the number of primes is infinite. [35] When n ! ± 1 {\displaystyle n!\pm 1} is itself prime it is called a factorial prime ; [ 36 ] relatedly, Brocard's problem , also posed by Srinivasa Ramanujan ...

  3. Stirling's approximation - Wikipedia

    en.wikipedia.org/wiki/Stirling's_approximation

    One way of stating the approximation involves the logarithm of the factorial: ⁡ (!) = ⁡ + (⁡), where the big O notation means that, for all sufficiently large values of , the difference between ⁡ (!

  4. Large numbers - Wikipedia

    en.wikipedia.org/wiki/Large_numbers

    Large numbers, far beyond those ... Combinatorial processes give rise to astonishingly large numbers. The factorial function, which quantifies permutations of a fixed ...

  5. 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, for example the Lucas–Lehmer primality test for Mersenne numbers. “!” is the factorial, “#” is the primorial, and () is the third cyclotomic polynomial, defined as + +.

  6. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k).

  7. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    Even numbers are always 0, 2, or 4 more than a multiple of 6, while odd numbers are always 1, 3, or 5 more than a multiple of 6. Well, one of those three possibilities for odd numbers causes an issue.

  8. Googol - Wikipedia

    en.wikipedia.org/wiki/Googol

    A googol is the large number 10 100 or ten to the power of one hundred. ... (factorial of 70). Using an integral, binary numeral system, one would need 333 ...

  9. Integer factorization records - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization_records

    Integer factorization is the process of determining which prime numbers divide a given positive integer.Doing this quickly has applications in cryptography.The difficulty depends on both the size and form of the number and its prime factors; it is currently very difficult to factorize large semiprimes (and, indeed, most numbers that have no small factors).