# Check whether a number is prime, composite numbers prime factorization (prime decomposition) as products of factors in exponential form

## Latest factored numbers

 30 = 2 × 3 × 5 Jun 19 05:21 UTC (GMT) 1,382 = 2 × 691 Jun 19 05:21 UTC (GMT) 432 = 24 × 33 Jun 19 05:21 UTC (GMT) 1,245,607 = 11 × 17 × 6661 Jun 19 05:21 UTC (GMT) 617 is a prime number, it cannot be prime factorized into other prime factors Jun 19 05:20 UTC (GMT) 9,316 = 22 × 17 × 137 Jun 19 05:20 UTC (GMT) 30,352,152,522 = 2 × 3 × 5058692087 Jun 19 05:20 UTC (GMT) 544,496 = 24 × 34031 Jun 19 05:20 UTC (GMT) 2,777,777,543 = 172 × 9611687 Jun 19 05:20 UTC (GMT) 5,862,269 = 7 × 837467 Jun 19 05:20 UTC (GMT) 440,446 = 2 × 191 × 1153 Jun 19 05:20 UTC (GMT) 2,147,483,646 = 2 × 32 × 7 × 11 × 31 × 151 × 331 Jun 19 05:20 UTC (GMT) 118 = 2 × 59 Jun 19 05:19 UTC (GMT) see more... integer numbers factored down to their prime factors

## Prime numbers definition. Composite numbers

#### A composite number is a positive integer that has at least one positive divisor other than 1 and the number itself. A composite number is also any positive integer larger than 1 that is not a prime number.

• 2 is divisible only by 2 and 1, so 2 is a prime number
• 3 is divisible only by 3 and 1, so 3 is a prime number
• 5 is divisible only by 5 and 1, so 5 is a prime number
• 13 is divisible only by 13 and 1, so 13 is a prime number

#### 1 is not considered prime, so the first prime number is 2 (prime numbers list is starting with the number 2)

##### The fundamental theorem of arithmetic says that every integer larger than 1 can be written as a product of one or more prime numbers in a way that is unique, except for the order of the prime factors. Prime numbers are thus the basic building blocks of all numbers. If 1 were admitted as a prime, number 15 for example could be factored as 3 × 5 and 1 × 3 × 5; these two representations would be considered different prime factorizations of 15 (prime factorization into prime factors), so the statement of the theorem would have to be modified.
• 4 is divisible by 4, 2 and 1, so 4 is not a prime number, it's a composite number; 4 = 22
• 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime number, it's a composite number; 6 = 2 × 3
• 8 is divisible by 8, 4, 2 and 1, so 8 is not a prime number, it's a composite number; 8 = 23
• 9 is divisible by 9, 3, and 1, so 9 is not a prime number, it's a composite number; 9 = 32

Examples of prime numbers, up to 100: 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