# Category:Prime Numbers

A **prime number** is defined as a positive integer which has exactly two factors: one and itself. A factor of a number is an integer which divides evenly into it--that is, divides with a remainder of zero. By this definition one and zero are not prime. One only has one factor (which is itself), and zero divided by any number always has a remainder of zero, so it effectively has an infinite number of factors.

Primality is frequently used for instructional purposes in computer science. Naive algorithms for calculating it are usually complex enough to be a test for a new programmer (barring algorithms built into languages), but simple enough that they can be used as parts of problems to follow.

Below is a list of tasks which involve:

- the calculation (or generation) of primes or
*types*of primes - the use of primes in finding other types of numbers
- the factorization of integers
- the determination of divisibility of integers
- the use of various algorithms in finding or detecting primes or types of primes
- the coding of various types of primality tests
- the use of primes in generating various (number) sequences
- etc.

- the calculation (or generation) of primes or

## Pages in category "Prime Numbers"

The following 114 pages are in this category, out of 114 total.

### A

### C

- Carmichael 3 strong pseudoprimes
- Carmichael lambda function
- Chernick's Carmichael numbers
- Chowla numbers
- Circular primes
- Concatenate two primes is also prime
- Consecutive primes with ascending or descending differences
- Coprime triplets
- Coprimes
- Count in factors
- Cousin primes
- Cuban primes
- Cubic special primes
- Cyclops numbers

### F

### L

### M

### N

### P

- Palindromic primes
- Palindromic primes in base 16
- Pandigital prime
- Partition an integer x into n primes
- Perfect numbers
- Pernicious numbers
- Pierpont primes
- Piprimes
- Pisano period
- Primality by trial division
- Primality by Wilson's theorem
- Prime conspiracy
- Prime decomposition
- Prime numbers which contain 123
- Prime triplets
- Prime words
- Primes - allocate descendants to their ancestors
- Primes which contain only one odd digit
- Primes whose first and last number is 3
- Primes whose sum of digits is 25
- Primes with digits in nondecreasing order
- Primorial numbers
- Proper divisors

### S

- Safe and Sophie Germain primes
- Safe primes and unsafe primes
- Semiprime
- Sequence of primes by trial division
- Sequence of primorial primes
- Sexy primes
- Sieve of Eratosthenes
- Sieve of Pritchard
- Smarandache prime-digital sequence
- Special neighbor primes
- Square form factorization
- Strange numbers
- Strange plus numbers
- Strange unique prime triplets
- Strong and weak primes
- Substring primes
- Successive prime differences
- Sum of primes in odd positions is prime