Prime Numbers

A prime number is a number that is greater than 1 and that is not a product of two smaller numbers. A number greater than 1 that is not a prime number is called a composite number.

For an example 5 is a prime number because the only way of writing it with integer factorization we get: 1 x 5 or 5 x 1, which involves only 5 itself. On the contrary 4 is not a prime number because we can factor it as: 1 x 4, 2 x 2, and 4 x 1.

Finding prime numbers manually is not only tedious, but can also be considered impossible once we get to larger numbers such as the current largest known prime number which has 24,862,048 digits. Being that numbers are infinite the list of prime numbers is also infinite, as demonstrated by Euclid in 300 BC. For this reason there are many formulas for finding prime numbers such as prime factorization.

Because I often have to reference this here are the first 100 prime numbers:

	1	2	3	4	5	6	7	8	9	10
1-10	2	3	5	7	11	13	17	19	23	29
11-20	31	37	41	43	47	53	59	61	67	71
21-30	73	79	83	89	97	101	103	107	109	113
31-40	127	131	137	139	149	151	157	163	167	173
41-50	179	181	191	193	197	199	211	223	227	229
51-60	233	239	241	251	257	263	269	271	277	281
61-70	283	293	307	311	313	317	331	337	347	349
71-80	353	359	367	373	379	383	389	397	401	409
81-90	419	421	431	433	439	443	449	457	461	463
91-100	467	479	487	491	499	503	509	521	523	541