07-23-2026, 10:25 PM
Emirp
Summary
An emirp is a fascinating type of prime number that reveals an unexpected symmetry in mathematics: when its digits are reversed, the result is a different prime number. The name “emirp” comes from reversing the word “prime,” and these numbers are also known as reversible primes. Unlike palindromic primes, which remain the same when reversed (such as 101), emirps must transform into another distinct prime. The first examples are 13, 17, 31, 37, 71, 73, 79, and 97, where reversing the digits creates another valid prime.
Emirps are important because they demonstrate how simple operations, such as rearranging digits, can create interesting structures within the world of prime numbers, which are already among the most mysterious objects in number theory. They are studied in recreational mathematics, computational searches, and investigations of prime patterns, showing how even basic numerical ideas can lead to deep questions about order and randomness. The concept was named by mathematician Jeremiah Farrell, and emirps are included in mathematical databases such as the OEIS sequence A006567.
Major key takeaways:
ARTICLE
Summary
An emirp is a fascinating type of prime number that reveals an unexpected symmetry in mathematics: when its digits are reversed, the result is a different prime number. The name “emirp” comes from reversing the word “prime,” and these numbers are also known as reversible primes. Unlike palindromic primes, which remain the same when reversed (such as 101), emirps must transform into another distinct prime. The first examples are 13, 17, 31, 37, 71, 73, 79, and 97, where reversing the digits creates another valid prime.
Emirps are important because they demonstrate how simple operations, such as rearranging digits, can create interesting structures within the world of prime numbers, which are already among the most mysterious objects in number theory. They are studied in recreational mathematics, computational searches, and investigations of prime patterns, showing how even basic numerical ideas can lead to deep questions about order and randomness. The concept was named by mathematician Jeremiah Farrell, and emirps are included in mathematical databases such as the OEIS sequence A006567.
Major key takeaways:
- An emirp is a prime number whose digit reversal is a different prime.
- It excludes palindromic primes that remain unchanged.
- Early examples include 13, 17, 31, and 37.
- Emirps highlight the beauty of hidden patterns in prime numbers.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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