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 Divisibility Prime numbers A prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. Prime numbers are: 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,... The number 1 is by definition not a prime number. A composite number is a whole number greater than one that has more than two factors. Composite numbers are: 4, 6, 8, 9, 10, 12, 14, 15,... Choose the prime number127 129 715 943 A simple ancient algorithm for finding all prime numbers up to a specified integer, n, is the Sieve of Eratosthenes: Write down the numbers 1, 2, 3, ..., n. We will eliminate composites by marking them. Initially all numbers are unmarked. Mark the number 1 as special (it is neither prime nor composite). Cross out all numbers >2 which are divisible by 2 (every second number). Find the smallest remaining number >2. It is 3. So cross out all numbers >3 which are divisible by 3 (every third number). Find the smallest remaining number >3. It is 5. So cross out all numbers >5 which are divisible by 5 (every fifth number). Continue until you have crossed out all numbers divisible by Put the remaining unmarked numbers in the sequence on your list of prime numbers.