Two prime numbers that differ by 2. 11 and 13 are prime twins, as are 59 and 61.
Prime twins (also called twin primes) are pairs of prime numbers that are exactly 2 apart. Since both numbers are prime and separated only by a single even number, they are as close together as two odd primes can be.
Some examples of prime twins:
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3 and 5
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5 and 7
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11 and 13
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17 and 19
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29 and 31
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59 and 61
Notice that every pair of prime twins (beyond 3 and 5) is separated by an even number, which makes sense because all even numbers greater than 2 are composite, so they can never be prime themselves.
Whether there are infinitely many prime twins is one of the most famous unsolved problems in mathematics. Mathematicians strongly suspect the answer is yes, but no one has been able to prove it yet. This open question, known as the “Twin Prime Conjecture,” shows that even simple-sounding ideas in number theory can lead to deep, unresolved mysteries.
When Do Students Learn About Prime Twins?
Students encounter prime twins after building a solid understanding of prime numbers and factors.
Grades 4–6 – Prime Numbers and Factors
Students identify prime numbers and explore their properties, laying the groundwork for recognizing patterns like prime twins.
Grades 9+ – Prime Twins in Number Theory
Students encounter prime twins in discussions of number theory, mathematical conjectures, and the deeper structure of prime numbers.
