Palindrome Number Checker

Reads same forwards & backwards

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About Palindrome Number Checker

A palindrome number checker testing if n reads the same in both directions. Supports multiple bases (2-16). Shows reverse, next palindrome, and counts palindromes in ranges. Also tests the 196 conjecture. All calculations are client-side.

Palindrome Number Checker Features

  • Palindrome check
  • Multi-base
  • Next palindrome
  • 196 conjecture
  • Range count
Palindromic number: reads same left-to-right and right-to-left. 121, 1331, 12321. In binary: 5=101, 9=1001. Every number in base 10 can become a palindrome by the reverse-and-add process (unproven: 196 might not).

How to Use

Enter n:

  • Palindrome: Same forwards/backwards
  • Base: Check in any base 2-16
  • Next: Find next palindrome

196 Conjecture

The reverse-and-add process: 68→68+86=154→154+451=605→605+506=1111 (palindrome!). The number 196 hasn't converged after billions of iterations. It's conjectured to never produce a palindrome.

Properties

  • All 1-digit numbers are palindromes
  • Palindromic primes: 2,3,5,7,11,101,131...
  • There are no palindromic numbers with even digits that are prime (except 11)

Step-by-Step Instructions

  1. 1Enter n.
  2. 2Check palindrome.
  3. 3Try other bases.
  4. 4Find next palindrome.
  5. 5Test reverse-and-add.

Palindrome Number Checker — Frequently Asked Questions

What is the 196 conjecture?+

Starting from 196, repeatedly reverse digits and add: 196+691=887, 887+788=1675, 1675+5761=7436, ... After billions of iterations and trillions of digits, no palindrome has been found. It's believed 196 is a Lychrel number (never reaches a palindrome), but this is unproved.

How many palindromes are there below N?+

Below 10ⁿ, there are approximately 2·10^(n/2) palindromes. The density of palindromes goes to 0 but they're still infinite. There are 9 one-digit, 9 two-digit, 90 three-digit, 90 four-digit palindromes.

Can a palindrome be a palindrome in multiple bases?+

Yes! 585 = 1001001001 in base 2 (also palindromic). Numbers that are palindromic in multiple bases are rare and interesting. 1 is palindromic in every base.

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