Prime Numbers:

A prime numbers is a number greater than one whose factors are only one and itself. In other words, 4 is not prime, because its factors are 1, 2 and 4 (1x4, 2x2). But 5 is prime, because the only way you can get a product of 5 is by multiplying 1 and 5 (1x5). Composite numbers are those who has more than two factors. The number 1 is not prime OR composite because it has only one factor.
Here are all the prime numbers up to 500:
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, ...
How to find big Prime Numbers:
Following is a somewhat celebrated result of Euler:
The function f(x) = x^2 + x + 41 is always prime for x = 0, 1 ,..., 39.
This quadratic was the record holder for centuries as a consecutive,
Distinct quadratic prime-producer for an initial range of input
Values. It is not, however, the new function is there that can give more range of prime numbers than Euler’s:
The Function:
f(x) = 36x^2 - 810x + 2753
Which is always prime for x = 0, 1, ... , 44.