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2. List of prime numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_prime_numbers

   Some sequences have alternate names: 4n+1 are Pythagorean primes, 4n+3 are the integer Gaussian primes, and 6n+5 are the Eisenstein primes (with 2 omitted). The classes 10 n + d ( d = 1, 3, 7, 9) are primes ending in the decimal digit d .

3. 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 2p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 22 − 1.

4. Collatz conjecture - Wikipedia

   en.wikipedia.org/wiki/Collatz_conjecture

   For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...

5. Circular prime - Wikipedia

   en.wikipedia.org/wiki/Circular_prime

   A circular prime is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will be prime. [1] [2] For example, 1193 is a circular prime, since 1931, 9311 and 3119 all are also prime. [3] A circular prime with at least two digits can only consist of combinations of the ...

6. Benford's law - Wikipedia

   en.wikipedia.org/wiki/Benford's_law

   For b = 2, 1 (the binary and unary) number systems, Benford's law is true but trivial: All binary and unary numbers (except for 0 or the empty set) start with the digit 1. (On the other hand, the generalization of Benford's law to second and later digits is not trivial, even for binary numbers.

7. Mnemonic major system - Wikipedia

   en.wikipedia.org/wiki/Mnemonic_major_system

   The major system (also called the phonetic number system, phonetic mnemonic system, or Herigone's mnemonic system) is a mnemonic technique used to help in memorizing numbers. The system works by converting numbers into consonants, then into words by adding vowels. The system works on the principle that images can be remembered more easily than ...

8. Lucky number - Wikipedia

   en.wikipedia.org/wiki/Lucky_number

   Lucky number. In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers). [1]

9. Kaprekar's routine - Wikipedia

   en.wikipedia.org/wiki/Kaprekar's_routine

   Kaprekar's routine. In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers. As an example, starting with the number 8991 in ...