4201

4201 is a positive integer. In mathematics, it is a prime number, meaning its only positive divisors are 1 and itself. It is odd and not divisible by any prime less than or equal to 61, which covers all potential divisors up to its square root (approximately 64.8). It is congruent to 1 modulo 4, a property that implies, by Fermat's two-square theorem, that 4201 can be expressed as the sum of two squares; indeed 4201 = 51^2 + 40^2.

In other base representations, 4201 is 0x1069 in hexadecimal and 0b1000001101001 in binary. The decimal digits sum to 7, and its digital root is also 7. As a prime, Euler's totient function yields φ(4201) = 4200.

Beyond its basic arithmetic properties, 4201 has a simple representation in the Gaussian integers: 4201 factors as (51 + 40i)(51 − 40i). This illustrates how primes congruent to 1 modulo 4 can be expressed as a sum of two squares and correspond to a pair of complex conjugate factors in the Gaussian integers.

There are no widely recognized constants, theorems, or named sequences inherently associated with the number 4201. It remains a relatively small prime of interest primarily within elementary number theory and numerical base representations.