Euler Problem 4: Largest Palindromic Product

Euler Problem 4 Definition

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.


This code searches fo palindromic numbers, starting at the highest values. The palindromes are tested by converting the number to a character string. When the first palindromic number is found, the loop is broken.

# Cycles through all number combinations, starting at 999
for (i in 999:900) {
    for (j in 990:900) {
        word <- as.character(i * j)
        # Create reverse
        reverse <- paste(rev(unlist(strsplit(word, ""))), collapse = "")
        # Check whether palindrome
        palindrome <- word == reverse
        if (palindrome) 
    if (palindrome) {
answer <- i * j

This code on GitHub.

Searching a bit further results in twelve palindromic numbers. Sequence A002113 in the OEIS lists palindromes in base 10. Mathematicians used these numbers only for fun, without any purpose in reality. The graph below shows the number of palindromic numbers between 0 and 1 million.

Euler Problem 4 : Palindromic numbers

Palindromic number count

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