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Prime Numbers

Answer each question about prime numbers — list, test, pair, factor, or find the number as asked.

Example

List all the prime numbers less than 40.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
  1. 1.

    List all the prime numbers less than 60.
  2. 2.

    Write 96 as a product of prime factors.
  3. 3.

    Find every pair of prime numbers whose product is 38.
  4. 4.

    Discover. List the factor pairs of 36 in order:   (1, 36)   (2, 18)   (3,   )   (4,   )   (6,   ).

    What do you notice about where the pairs fold — and how far must you check to find every factor of a number?

    Use it. Is 229 prime? Check divisors only up to √229 (about 15): test 2, 3, 5, 7, 11, 13.
  5. 5.

    What is the smallest two-digit prime such that both its digits are prime?