# 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 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 75 pages are in this category, out of 75 total.

### C

### F

### N

### P

- Palindromic primes
- 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 triplets
- Primes - allocate descendants to their ancestors
- Primes which sum of digits is 25
- Primes with digits in nondecreasing order
- Primorial numbers
- Proper divisors

### S

- Safe primes and unsafe primes
- Semiprime
- Sequence of primes by trial division
- Sequence of primorial primes
- Sexy primes
- Sieve of Eratosthenes
- Smarandache prime-digital sequence
- Square Form Factorization
- Strange numbers
- Strange plus numbers
- Strong and weak primes
- Substring primes
- Successive prime differences