3961

3961 is an integer in the decimal system, sitting between 3960 and 3962. It is an odd, composite number.

In terms of prime factorization, 3961 = 17 × 233, making it a semiprime (the product of two primes). Both factors are congruent to 1 modulo 4 (17 ≡ 1 mod 4 and 233 ≡ 1 mod 4), which by Fermat’s two-square theorem implies that 3961 can be expressed as a sum of two squares. Indeed, 3961 = 60^2 + 19^2.

Numerical representations aside from decimal include its binary and hexadecimal forms: 3961 in binary is 111101111001, and in hexadecimal it is 0xF79. The number has a digital root of 1 (since 3 + 9 + 6 + 1 = 19, and 1 + 9 = 10, 1 + 0 = 1), and it is not divisible by 3 or 9, making it not a Harshad number. It also satisfies 3961 ≡ 1 (mod 4) and 3961 ≡ 1 (mod 8). Geometrically, 3961 is close to a perfect square: 63^2 = 3969, so 3961 = 63^2 − 8.

A notable contextual link is that 233, one of its prime factors, is a Fibonacci number (the 13th, F13). The product 17 × 233 thus connects a small prime with a Fibonacci prime within the factorization of 3961.

If treated as a year designation, 3961 would refer to a year in the distant future. In mathematics and number theory, 3961 is primarily noted for its semiprime structure and its sum-of-squares representation.