This number is a prime.
The first three digits in the decimal expansion of the Euler-Mascheroni constant (gamma = 0.5772156649...). It is not yet known if the constant is a rational number, i.e., the ratio of two integers a/b. [Kulsha]
The larger of only two 3-digit primes that remain prime when inserting one, two or three zeros between each digit, i.e., 50707, 5007007, 500070007 are primes. The other such prime is 131. [Loungrides]
The smallest prime that can be expressed as sum of powers with the even digits as bases and exponents, i.e., 0^6+2^8+4^4+6^0+8^2 = 577. [Loungrides]
The larger of only two primes p, smaller than a thousand, such that p and p^3 have the same sum of digits. The other is 487. [Loungrides]
The solution to x2 - 2y2 = 1, where y = 408. [Baudhayana]
The 17th Pierpond prime, (form 2^u*3^v+1), is the largest prime-digit Pierpond prime, i.e., 577 = 2^6*3^2+1. [Loungrides]
The sum of the first 577 positive Cyclops numbers is divisible by 577. [Gaydos]