160001

160001 is a natural number that follows 160000 and precedes 160002. It is an odd integer and, by prime testing, appears to be prime. In particular, 160001 can be expressed as 400^2 + 1^2, which shows it is the sum of two squares. This representation aligns with the Frobenius–Lagrange idea that a prime congruent to 1 modulo 4 can be written as a sum of two squares; indeed, 160001 ≡ 1 (mod 4).

In decimal notation, 160001 is the standard form most readers will encounter. The number does not bear widely recognized historical or scientific significance beyond its properties as a prime and as a sum of two squares. As with many primes of this size, it is mainly of interest within the context of number theory, primality testing, and numerical examples illustrating concepts such as trial division and modular arithmetic.

Verification of its primality involves checking divisibility by all primes up to 397, since the square root of 160001 is just over 400. No divisor is found in that range, confirming that 160001 is prime. As a prime, it is a member of various numerical sequences and serves as a data point in the study of primes near the five- to six-figure range.