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25 primes.
Yes, there are an infinite number of twin primes.
There are not three odd primes with the sum of 14. The sum of three odd primes will be an odd number.
To find twin primes of a given number, iterate through the numbers starting from the given number, and for each number, check if both the number and the number+2 are prime. If they are, then they form a pair of twin primes with the given number.
743 is a prime number.