3003003

3003003 is a natural number in base ten that has attracted attention for its symmetry and arithmetic properties. The number is a palindrome, read the same forwards and backwards, and its digit sum equals nine, making it divisible by 3. It is not a prime; its factorization begins with \(3^2 = 9\), after which the remaining factor \(333\,667\) is believed to be prime, though its primality has not been universally verified for all large sub‑factors.

Mathematically, 3003003 is also interesting as a product of consecutive integers: it equals \(3\,003\,003 = 3 \times 1\,001\,001 = 3 \times 3 \times 333\,667\). This ties it to the sequence of centered triangular numbers and places it among a small set of numbers that are both palindromic and highly divisible. In base ten, it has seven digits, an odd number of digits, and its mirrored halves contain a repeated pattern of zeros and threes that makes it visually striking. In binary representation, the number is 101101111100010110110, a string that also demonstrates regularity in digit grouping.

Outside pure number theory, 3003003 has been used as an identifier in a few cataloguing systems. For example, it appears as a catalogue number for a minor planet in the Minor Planet Center’s database, although the specific object reference is by its provisional designation. In some software development environments, the value 3003003 is occasionally employed as a sentinel or magic number in legacy code bases, chosen for its recognizability among programmers familiar with its palindromic property.

Overall, 3003003 is a modest but illustrative example of how simple numerical patterns can intersect with larger mathematical themes and practical applications.