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2. 84 (number) - Wikipedia

   en.wikipedia.org/wiki/84_(number)

   As no smaller number has more than 12 divisors, 84 is a largely composite number. [7] The twenty-second unique prime in decimal, with notably different digits than its preceding (and known following) terms in the same sequence, contains a total of 84 digits. [8] A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces. [9]

3. Table of prime factors - Wikipedia

   en.wikipedia.org/wiki/Table_of_prime_factors

   m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...

4. List of prime numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_prime_numbers

   All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.

5. Amicable numbers - Wikipedia

   en.wikipedia.org/wiki/Amicable_numbers

   However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. [8] Also, every known pair shares at least one common prime factor. It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 65.

6. Friendly number - Wikipedia

   en.wikipedia.org/wiki/Friendly_number

   [2] [3] J.Ward [4] proved that any positive integer other than 10 with abundancy index 9/5 must be a square with at least six distinct prime factors, the smallest being 5. Further, at least one of the prime factors must be congruent to 1 modulo 3 and appear with an exponent congruent to 2 modulo 6 in the prime power factorization of n ...

7. 83 (number) - Wikipedia

   en.wikipedia.org/wiki/83_(number)

   83 is: . the sum of three consecutive primes (23 + 29 + 31). the sum of five consecutive primes (11 + 13 + 17 + 19 + 23). the 23rd prime number, following 79 (of which it is also a cousin prime) and preceding 89.

8. Greatest common divisor - Wikipedia

   en.wikipedia.org/wiki/Greatest_common_divisor

   [9] [10] [11] This convention is followed by many computer algebra systems. [12] Nonetheless, some authors leave gcd(0, 0) undefined. [13] The GCD of a and b is their greatest positive common divisor in the preorder relation of divisibility. This means that the common divisors of a and b are exactly the divisors of their GCD.

9. Fermat's factorization method - Wikipedia

   en.wikipedia.org/wiki/Fermat's_factorization_method

   For example, to factor =, the first try for a is the square root of 5959 rounded up to the next integer, which is 78. Then b 2 = 78 2 − 5959 = 125 {\displaystyle b^{2}=78^{2}-5959=125} . Since 125 is not a square, a second try is made by increasing the value of a by 1.