# palindromic prime

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

30203

133020331

1713302033171

12171330203317121

151217133020331712151

1815121713302033171215181

16181512171330203317121518161

331618151217133020331712151816133

9333161815121713302033171215181613339

11933316181512171330203317121518161333911

**See Also:** Strobogrammatic, Tetradic

**Related pages** (outside of this work)

- Top 20 palindromic primes
- Selected palidromic primes with more than 1000 digits
- Palindromic prime ZIP Codes

**References:**

- DO94
H. DubnerandR. Ondrejka, "A PRIMEr on palindromes,"J. Recreational Math.,26:4 (1994) 256--267.- GC1969
H. GabaiandD. Coogan, "On palindromes and palindromic primes,"Math. Mag.,42(1969) 252--254.MR0253979- HC2000
G. L. Honaker, Jr.andC. Caldwell, "Palindromic prime pyramids,"J. Recreational Math.,30:3 (1999-2000) 169--176.- Iseki1988
Iséki, Kiyoshi, "Palindromic prime numbers from experimental number theory,"Math. Japon.,33:5 (1988) 715--720.MR 972382- Iseki1988b
Iséki, Kiyoshi, "Palindromic prime numbers,"Math. Japon.,33:6 (1988) 861--862.MR 975864- Iseki1988c
Iséki, Kiyoshi, "Palindromic prime numbers from experimental number theory. II,"Math. Japon.,33:6 (1988) 863--872.MR 975865- McDaniel87b
W. McDaniel, "Palindromic Smith numbers,"J. Recreational Math.,19:1 (1987) 34--37.- Ribenboim95
P. Ribenboim,The new book of prime number records, 3rd edition, Springer-Verlag, 1995. New York, NY, pp. xxiv+541, ISBN 0-387-94457-5.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 seventy-five pages.]

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