7229

7229 is a prime number in the set of natural numbers. It is odd and greater than 1000, and its only positive divisors are 1 and 7229.

In different numeral systems, 7229 has the following representations: binary 1110000111101, hexadecimal 0x1C3D, and octal 16075. Decimal digits are 7, 2, 2, and 9, with a digit sum of 20. The number ends in 9, is congruent to 1 modulo 4, and is congruent to 5 modulo 6, which aligns with common properties of odd primes greater than 3.

Mathematics and number theory note that any prime p with p ≡ 1 (mod 4) can be expressed as a sum of two squares. For 7229, one such representation is 7229 = 85^2 + 2^2, since 85^2 = 7225 and 2^2 = 4. This reflects Fermat’s theorem on sums of two squares and confirms a classic property of primes in this congruence class.

Because 7229 is prime, it has no nontrivial factorization into integers other than 1 and itself. Its prime nature and its representation in various bases are the primary mathematical notes commonly associated with the number.

In summary, 7229 is a prime with multiple base representations and a known sum-of-squares expression, illustrating typical structural features of primes congruent to 1 modulo 4.