Create Number Palindrome
Create palindromes from any number - 5 modes including mirror, reverse-and-add (196 problem), next/previous palindrome. BigInt precision. Free.
Create palindromes from any number using 5 modes: mirror-odd, mirror-even (duplicate center), reverse-and-add (196 problem), next palindrome ≥ N, or previous palindrome ≤ N. BigInt support for arbitrary precision.
How to Use Create Number Palindrome
- Type a number. Negatives and decimals are accepted. Live count shows digit total.
- Pick mode. Mirror-odd = mirror without duplicating the center (123 → 12321, length 2n-1). Mirror-even = full mirror duplicating the center (123 → 123321, length 2n). Reverse-and-add = iteratively reverse-and-sum until a palindrome appears (196 problem). Next/Previous palindrome = search the integer line.
- Toggle "Preserve negative sign" to keep the minus in output. Toggle "Preserve decimal point" to reinsert
.at the original position in mirror modes (the digit count grows but the decimal position stays put). - Click Create (or Ctrl+Enter). Result + stats + (for reverse-and-add) the full iteration trail appear below.
Frequently Asked Questions
What are palindromic dates?
Dates whose digits read the same backward, like 22/02/2022 or 12/02/2021 in day-month-year format. They are a fun corner of recreational math: the format matters (02/12/2021 is palindromic in DD/MM/YYYY but not MM/DD/YYYY), full 8-digit palindromic dates are rare, and people schedule weddings and product launches around them. You can verify any date candidate by typing its digits into this tool.
What’s the difference between mirror-odd and mirror-even?
Mirror-odd reflects without duplicating the center: 123 → 12321 (5 digits). Mirror-even reflects and duplicates: 123 → 123321 (6 digits). Both are valid palindromes; pick based on whether you want odd or even length.
What’s the “196 problem”?
Take a number. Reverse its digits. Add the reverse to the original. Check if the result is a palindrome. If not, repeat with the new number. Most numbers reach a palindrome in a handful of steps (89 takes 24 iterations). 196 itself has been computed through 700 million iterations without reaching a palindrome – it’s a Lychrel candidate. The tool caps at 1000 iterations and reports “likely Lychrel” if no palindrome appears. This is not a mathematical proof – just exceeded the cap.
What happens to negative numbers?
The sign is separated from the digits before processing. After the palindrome is built, the minus is reattached if the “Preserve negative sign” checkbox is on (default). Note: mathematically, -12321 is still a “palindrome of digits” but isn’t equal to its own integer-reverse – palindrome-ness here is purely lexical, not numerical-magnitude.
What about decimals?
The decimal point is separated from the digits. In mirror modes, you can reinsert the decimal at the original integer-part length: 1.23 mirror-odd becomes 1.2321 (decimal between original int part and the mirror). In reverse-and-add and next/previous modes, the decimal is dropped (these are integer operations).
How is “next palindrome” computed?
Iteratively increment by 1 and test, up to a 10⁹ safety cap. For inputs like 12345, the answer (12421) is 76 increments away. For huge inputs with no palindrome nearby, the search would be slow – there’s a smarter analytical algorithm for huge inputs that constructs the next palindrome by mirroring the first half + 1, but the simple loop is fine for typical use.
Is single-digit input already a palindrome?
Yes – any 1-digit number reads the same forwards and backwards. Mirror modes return the digit unchanged. Reverse-and-add returns the digit unchanged. Next/Previous return the digit unchanged.
Are palindromes used in real applications?
Yes – palindrome checks appear in algorithm interviews (LeetCode 9, 125, 234), DNA sequence analysis (reverse complements), error-detection in barcodes, and recreational number theory. Lychrel numbers are an open mathematics problem.
Is anything uploaded?
No. Pure browser-side BigInt arithmetic. Your input never leaves your device.