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. Dubner and R. Ondrejka, "A PRIMEr on palindromes," J. Recreational Math., 26:4 (1994) 256--267.
- GC1969
- H. Gabai and D. Coogan, "On palindromes and palindromic primes," Math. Mag., 42 (1969) 252--254. MR0253979
- HC2000
- G. L. Honaker, Jr. and C. 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, New York, NY, 1995. 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.]
Printed from the PrimePages <t5k.org> © Reginald McLean.