Reflect back on Palindrome Days!

palindrome examples

All Grades

Palindrome days happen when the numbers on the calendar are the same forward and backward. Previously we posted Celebrate Palindrome Days with genetics and chromosome activities. Depending on date formats, palindromic dates can be pretty rare. So, what are the odds that we’d be writing about another Palindrome day? When calculated in the mm-dd-yyyy format, Palindrome Days tend to occur only in the first few centuries of each millennium (1000 years).¹ That means we’re the lucky few who get to celebrate December 2, 2021 (12022021)! On the other hand, palindrome days using the m-dd-yy format are not as rare.

In any case, here are the palindrome dates for the next few decades so that you can plan ahead:

But, palindromes don’t just exist on the calendar; they’re everywhere around us. In language, in math, and science! So, palindrome dates are the perfect time to introduce your students to the beauty of science in sequences all around us. Read on for some examples of palindromes in mathematics and fun ways to incorporate them in your lessons.

Meet our PALprime

In mathematics, a palindromic prime (aka a palprime) is a prime number that is also palindromic.

For example, Plateau and Depression Primes (aka PDPs) are palindromic in base 10 and consist of a repdigital (a number composed of repetition of a single digit) interior R, bordered by two identical single digits D different from the repdigit.

We get plateau primes when D < R, such as

1777771, 355555553, and 5(10¹⁴¹-1)/9 - 2(10¹⁴⁰+1)

We get depression primes when D > R, such as

72227, 722222227, 75557, 75555555557

Except for 11, all palindromic primes have an odd number of digits. The divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11. It is unknown if there are infinitely many palindromic primes in base 10.² The largest known as of October 2021 is

10^1888529 - 10⁹⁴⁴²⁶⁴ - 1.

Getting your students excited about palindromes is easy when they discover they’re all around us in nature, mathematics, and words. That’s what Fred Derf found after buying his first Racecar (hint: read that last sentence backward)!

References: 1. Time and Table: Aziz S. Inan University of Portland 2. Palindromic Primes - Prime Numbers.

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