Input three numbers to determine if they form a prime triplet, or specify a range to generate all prime triplets.
Prime Triplet Check or Generate
Result
Result
What Are Prime Triplets?
A prime triplet is a set of three consecutive prime numbers where the difference between the largest and smallest number is no more than 6. Examples include \( (3, 5, 7) \) and \( (11, 13, 17) \). In other words, if \( p \), \( q \), and \( r \) are all prime, and the difference \( r - p \leq 6 \), the set \( (p, q, r) \) forms a prime triplet.
How to Determine If Three Numbers Form a Prime Triplet
Verify primality: Check if all three numbers are prime.
Calculate the difference: Subtract the smallest number from the largest. If the difference is 6 or less, the numbers form a prime triplet. Otherwise, they are not a prime triplet.
Examples
Example 1: Are 5, 7, and 11 a Prime Triplet?
Solution:
Prime check: 5, 7, and 11 are all prime numbers.
Difference calculation: \( 11 - 5 = 6 \).
Result: Since all numbers are prime and the difference is 6 or less, \( (5, 7, 11) \) is a prime triplet.
Example 2: Are 1997, 1999, and 2003 a Prime Triplet?
Solution:
Prime check: 1997, 1999, and 2003 are all prime numbers.
Difference calculation: \( 2003 - 1997 = 6 \).
Result: All numbers are prime, and the difference is within the limit, so \( (1997, 1999, 2003) \) is a prime triplet.
Example 3: Are 31, 37, and 41 a Prime Triplet?
Solution:
Prime check: 31, 37, and 41 are all prime numbers.
Difference calculation: \( 41 - 31 = 10 \).
Result: The difference exceeds 6, so \( (31, 37, 41) \) is not a prime triplet.