Question 1193997: Q: Enter a prime triplet, where each member of the triplet is less than 100
I'm confused.
A prime triple is three consecutive primes, such that the first and the last differ by six.
(p, p+2, p+6)
(p, p+4, p+6)
(Examples: (5,7,11), (7,11,13), (11,13,17), (13,17,19) and (17,19,23).) These are prime triples.
However, I got the question wrong. It says the correct answer is 3,5,7
There are no prime triplets other than 3, 5, 7
Is the definition I considered wrong? Please explain. Thanks.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
Did you read the question correctly?
Your examples show that there are many prime triplets in which the difference between the first and last is 6.
The correct answer you show, "3,5,7", is the only prime triplet in which the difference between the first and last is LESS THAN 6.
That's because in any sequence of three consecutive odd numbers, one of them is divisible by 3. So the only prime triplet in which the difference between the first and last is LESS THEN 6 is the triplet that includes the prime number 3.
So, given the answer you show, I suspect the problem asks for the prime triplet(s) in which the difference between first and last is less than 6 -- not equal to 6.
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Based on your statement that the correct answer is "3,5,7", I assumed a prime triplet was a set of three consecutive prime numbers with a constant common difference.
Upon seeing that the definition of a prime triplet is a set of three consecutive primes in which the difference between the smallest and largest is 6, it is obvious that your "correct answer" is wrong, since the difference between the smallest and largest is only 4.
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