Palindrome Numbers and Mirror Numbers: Times, Dates and Curiosities

What Is a Palindrome?

A palindrome is a word, phrase or number that reads the same in both directions. The word comes from the Greek palin (“again”) and dromos (“course”), and was introduced into English by the writer Henry Peacham in 1638. For words, “radar”, “kayak” and “level” are examples; for phrases, one often quotes “Able was I ere I saw Elba”, ignoring spaces and accents.

The taste for palindromes is ancient. The famous Sator square (“SATOR AREPO TENET OPERA ROTAS”), a Latin formula found engraved at Pompeii, reads the same in four directions: it dates from the 1st century.

For numbers, the principle is the same: 1221, 2002, 15251. Do not confuse them with mirror numbers in the strict sense, such as 12 and 21, where one is the reversal of the other.

Palindrome Times

On a 24-hour dial, a time is a palindrome when its four digits read the same on either side: HH:MM with MM equal to HH written backwards. There are 16 per day. They should not be confused with the “double” times (HH = MM, such as 14:14): three times are both double and palindromic, 00:00, 11:11 and 22:22. Here are the sixteen, with a link to their page:

There is no palindrome time for the hours 06 to 09 nor for the hours 16 to 19: reversed, they would give 60 to 91 minutes, whereas minutes stop at 59. The sum of the four digits of a palindrome is always twice (a + b), so it is even before reduction. For these times, the middle is always a doubled digit: 01:10 contains “11”, 12:21 contains “22”, 13:31 contains “33”.

Palindrome Dates

A date is written as eight digits (DD/MM/YYYY). When these eight digits form a palindrome, the date is called a palindrome date. Between 2000 and 2030 there are nine, all in February:

The date 22/02/2022, a Tuesday, was nicknamed “Twosday” in English. As for palindrome years, the most recent is 2002; the next will be 2112: there are none between the two, which explains how rare the phenomenon is. A palindrome year has the form “abba”: for a = 2, there are only three (2002, 2112, 2222).

Mathematical Curiosities

Numerical palindromes have surprising properties, which you can check by hand.

• Multiples of 11. Every four-digit palindrome “abba” equals 1001 × a + 110 × b, that is 11 × (91a + 10b): it is therefore a multiple of 11. Example: 1221 = 11 × 111, 2002 = 11 × 182. It follows that 11 is the only prime palindrome with an even number of digits.
• Reverse and add. Start from a number, add its reversal, and repeat: most of the time you get a palindrome. 56 + 65 = 121 in one step; 59 gives 1111 in three steps (59 + 95 = 154, 154 + 451 = 605, 605 + 506 = 1111); 89 takes twenty-four steps and arrives at 8,813,200,023,188. The number 196 resists: it is suspected never to give a palindrome, without this having been proved.
• Prime mirror numbers. 13 and 31, 17 and 71, 37 and 73, 79 and 97 are pairs of prime numbers that are reversals of each other (called “emirps” in English).

Common Symbolic Readings

In popular numerology and among enthusiasts of angel numbers, a palindrome is read as a number of balance or of return: the same message on the way out and on the way back, a passage that folds back on itself. Authors often stress the centre of the number, seen as a pivot, and symmetry, seen as harmony.

This vocabulary comes from poetry more than from proof: no ancient numerological tradition founds it, and two books will give different meanings to 12:21. You can turn it into a game of reflection: what comes back in my day?

What Psychology Says

Palindromes are striking because our perception is very sensitive to symmetry. This makes 15:51 easier to notice than 15:47. Once spotted, we watch for it (frequency illusion) and we retain its appearances (confirmation bias).

Calculation puts things back in their place: the 16 palindrome minutes represent about 1.1% of the day, that is a one-in-90 chance at each glance. With some thirty glances a day, the probability of coming across at least one exceeds 28%. It is an ordinary encounter, not an event.

Playing With It, Without Turning It Into a Prediction

For fun: look for the next palindrome date on the calendar, or note the palindrome times you come across in a week. Do not look in a palindrome for the answer to a question about health, money or a relationship: it predicts nothing, and it designates no lottery number.

To continue: mirror times: how to read them, repeated digits, digit sequences and the guide to numerology.

Frequently asked questions

Also read

The meanings mentioned belong to tradition and symbolism. They are neither promises of results nor medical advice. Back to Guide to numerology and numbers.