121000001

121000001 is a natural number that lies between 120,999,999 and 121,000,002. In decimal notation it is written as 121,000,001. The number can be expressed as 11,000 squared plus one, i.e., 11,000^2 + 1. Consequently, it is not a perfect square.

As a nine-digit integer, 121000001 is odd and not divisible by 2 or 5. The sum of its digits is 5, so it is not divisible by 3. Since 11,000 is a multiple of 11, 11,000^2 is divisible by 11, and adding 1 yields a remainder of 1 modulo 11, so 121000001 is not divisible by 11. Because 11,000 is a multiple of 8, its square is a multiple of 64, meaning 121000001 ≡ 1 (mod 64). These simple checks establish that the number has no small prime divisors among 2, 3, 5, or 11, though a full primality test would require examining factors up to about 11,000.

Beyond these basic properties, 121000001 is primarily of interest as a large nine-digit integer with the form n^2 + 1 for n = 11,000. It does not have any widely recognized special constant, identity, or application in standard mathematical references. In general, it is treated as a numerical example rather than a named or canonical object.