Palindromic prime
In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such concerns. The first few decimal palindromic primes are:
- 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, … (sequence A002385 in the OEIS)
| Conjectured no. of terms | Infinite |
|---|---|
| First terms | 2, 3, 5, 7, 11, 101, 131, 151 |
| Largest known term | 101888529 - 10944264 - 1 |
| OEIS index |
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Except for 11, all palindromic primes have an odd number of digits, because the divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11. It is not known if there are infinitely many palindromic primes in base 10. The largest known as of October 2021 is
- 101888529 - 10944264 - 1.
which has 1,888,529 digits, and was found on 18 October 2021 by Ryan Propper and Serge Batalov. On the other hand, it is known that, for any base, almost all palindromic numbers are composite, i.e. the ratio between palindromic composites and all palindromes less than n tends to 1.