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A palindromic prime is simply a prime which is a palindrome. Obviously this depends on the base in which the number is written (for example, Mersenne primes
are palindromic base 2). When no radix is indicated, we assume the radix is 10.
In base ten a palindrome with an even number of digits is divisible by 11. So 11 is the only palindromic prime with an even number of digits.
As an example of palindromic primes, here is
a pyramid (list) of palindromic primes supplied by
G. L. Honaker, Jr.
2
30203
133020331
1713302033171
12171330203317121
151217133020331712151
1815121713302033171215181
16181512171330203317121518161
331618151217133020331712151816133
9333161815121713302033171215181613339
11933316181512171330203317121518161333911
See Also: Strobogrammatic, Tetradic Related pages (outside of this work) References:
 DO94
 H. Dubner and R. Ondrejka, "A PRIMEr on palindromes," J. Recreational Math., 26:4 (1994) 256267.
 GC1969
 H. Gabai and D. Coogan, "On palindromes and palindromic primes," Math. Mag., 42 (1969) 252254. MR0253979
 HC2000
 G. L. Honaker, Jr. and C. Caldwell, "Palindromic prime pyramids," J. Recreational Math., 30:3 (19992000) 169176. (Annotation available)
 Iseki1988
 Iséki, Kiyoshi, "Palindromic prime numbers from experimental number theory," Math. Japon., 33:5 (1988) 715720. MR 972382
 Iseki1988b
 Iséki, Kiyoshi, "Palindromic prime numbers," Math. Japon., 33:6 (1988) 861862. MR 975864
 Iseki1988c
 Iséki, Kiyoshi, "Palindromic prime numbers from experimental number theory. II," Math. Japon., 33:6 (1988) 863872. MR 975865
 McDaniel87b
 W. McDaniel, "Palindromic Smith numbers," J. Recreational Math., 19:1 (1987) 3437.
 Ribenboim95
 P. Ribenboim, The new book of prime number records, 3rd edition, SpringerVerlag, New York, NY, 1995. pp. xxiv+541, ISBN 0387944575. MR 96k:11112 [An excellent resource for those with some college mathematics. Basically a Guinness Book of World Records for primes with much of the relevant mathematics. The extensive bibliography is seventyfive pages.]
