Sexy primes are pairs of prime numbers that differ by 6. Examples include (5, 11), (11, 17), (17, 23), and so on. The term "sexy" comes from the Latin word "sex" for six. The question of whether there are infinitely many sexy primes is an open problem in number theory, meaning it has not yet been resolved.

Currently, there is no proof that there are infinitely many sexy prime pairs, similar to the situation with twin primes (pairs of primes that differ by 2). However, many mathematicians believe there are infinitely many such pairs, supported by heuristic arguments and computational evidence.

The belief is based on the probabilistic models of prime distribution, which suggest that primes occur with sufficient regularity to produce infinitely many pairs of primes with a given difference, including the difference of 6 for sexy primes.

### Questions for Further Exploration:

1. What are the probabilistic models used to estimate the distribution of prime numbers?
2. How do sexy primes relate to twin primes and cousin primes?
3. What are some famous unsolved problems in number theory related to prime numbers?
4. What are heuristic arguments in mathematics, and how are they applied to prime number conjectures?
5. Can you provide a list of the first ten sexy prime pairs?
6. What is the Twin Prime Conjecture, and how is it similar to the question about sexy primes?
7. How do mathematicians use computational methods to search for sexy prime pairs?
8. What are some known results or theorems related to prime gaps?

### Tip:
When studying prime numbers and their patterns, it is useful to explore both theoretical approaches and computational methods, as they often complement each other in advancing understanding and discovering new properties.

Discover the open problem in number theory: whether there are infinitely many sexy primes, prime pairs that differ by 6. Explore the probabilistic models of prime distribution and the similarities to twin primes. Learn about heuristic arguments in mathematics and computational methods used to study prime gaps.

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