Palindromic prime

A palindromical prime number is a prime number that reads the same when reversed.

Palindromical prime numbers include:

2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181, 18481, 19391, 19891, and 19991.

Out of the above list, 2 is the only number that is not an odd number. Almost all palindromic numbers are composite, for any base.

11 is the only palindromic prime with an even number of digits because all palindromic numbers with an even number of digits can be divided by 11, which means they are not primes.

The palindromic prime numbers have an infinite number, one of them can be created based on Smarandache function,^[1] and,^[2] etc. The known biggest palindromic prime so far is

10^1888529 - 10⁹⁴⁴²⁶⁴ - 1.

with 1,888,529 digits, found on 18 October 2021 by Propper and Batalov.^[3]

References

↑ Palindromes in Some Smarandache-Type Functions^{[permanent dead link]}, Hary Gunarto, S.M.S. Islam and A.A.K. Majumdar, Jurnal Matematika MANTIK Vol. 8, No. 1, June 2022, pp.1-9.
↑ See Caldwell, Prime Curios! (CreateSpace, 2009) p. 251, quoted in Wilkinson, Alec (February 2, 2015). "The Pursuit of Beauty". The New Yorker. Retrieved July 2, 2022.
↑ Chris Caldwell, The Top Twenty: Palindrome

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[1] Palindromes in Some Smarandache-Type Functions^{[permanent dead link]}, Hary Gunarto, S.M.S. Islam and A.A.K. Majumdar, Jurnal Matematika MANTIK Vol. 8, No. 1, June 2022, pp.1-9.

[2] See Caldwell, Prime Curios! (CreateSpace, 2009) p. 251, quoted in Wilkinson, Alec (February 2, 2015). "The Pursuit of Beauty". The New Yorker. Retrieved July 2, 2022.

[3] Chris Caldwell, The Top Twenty: Palindrome

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