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Yes, there are an infinite number of twin primes.
A twin prime pair are two primes separated by 2. For example, 3 and 5 are twin primes. It is conjectured that there are an infinite number of twin primes.
59 and 61 are twin primes.
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.
Six has four factors and is in between the twin primes 5 and 7.