3917

3917 is a natural number that follows 3916 and precedes 3918. In mathematics, it is notable for being a prime number, meaning it has no positive divisors other than 1 and itself.

In common numeral systems, 3917 is represented as binary 111101001101 and as hexadecimal 0xF4D. The sum of its decimal digits is 20, and it is congruent to 1 modulo 4.

Because 3917 is a prime congruent to 1 mod 4, it can be expressed as a sum of two squares: 3917 = 61^2 + 14^2. Consequently, in the Gaussian integers it factors as (61 + 14i)(61 − 14i). This demonstrates a standard property of primes p ≡ 1 (mod 4), which admit such a representation.

In Roman numerals, 3917 is written as MMMCMXVII. As a calendar year, 3917 CE would be in the distant future; there are no widely recognized historical events associated with that year in standard historical references.