Prime number

A prime number is a number which has exactly 2 factors.

A prime should be an odd number, with one exception, 2, as even numbers are multiples of 2, and 2 is.

Examples
5 is a prime number (in the right). It is a prime number as it has only 2 factors: 1 and itself.

Prime numbers to 1000 (see OEIS A000040)
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997


 * generated by a script. Click here to see the JavaScript code.

Mathematical properties
All prime numbers are deficient numbers. The sum of any prime number's proper divisor is 1, as the only proper divisor of a prime number is 1.

1 is not a prime number. Its sum of the proper divisors is 0.

Except for the cases 2 and 5, any number ending with these: 2, 4, 5, 6, 8 or 0 has to be composite.

The easiest method to find prime numbers is trial division. However, it takes the most time to calculate whether that number is prime or not. (This method is used in the script to generate primes from 1 to 1000.)

All prime numbers are positive integers.

Prime counting function
The prime counting function &pi;(n) is used to calculate the number of prime numbers from 1 to n.

However, $$\lim_{n\rightarrow\infty}\pi(n)\rightarrow0$$. This means almost no integers are prime (and almost all integers are composite).