Palindromic prime
| 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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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)
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. 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.
A few decorative examples do however exist; in base 10 the following are primes:
11, 122333221, and 1223334444555554444333221.
So are: 13331, and 12233355555333221.
For a large example, consider:
- 101888529 − 10944264 − 1,
which has 1,888,529 digits. It was found on 18 October 2021 by Ryan Propper and Serge Batalov.