Pick any two consecutive numbers in that range.
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A single number cannot be relatively prime. Any pair of numbers between 50 and 100 of which one is a prime will be relatively prime. There are 728 pairs of numbers that are relatively prime and I have neither the time nor patience to list them all!
To be relatively prime requires another number, and the highest common factor between 17 and that number must be 1. 17 is relatively prime to all numbers which are not multiples of 17 (since 17 is a prime number).
Any prime number is relatively prime to any other prime number.
Relatively prime numbers are numbers which share no common factors. This means the numbers are both the product of an entirely different set of prime numbers. There is no limit to the number of prime numbers. Thus there is no limit to the number of relatively prime pairs. Therefore there cannot be two "largest" relative primes.
No, twin primes are pairs of prime numbers that have only one number between them which is a composite number. For example, (3, 5) and (11, 13) are twin prime pairs with the composite number 4 and 12 respectively between them.