# 577

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]

577 is one of only two prime numbers with squares of the form AABCBC. Can you find the other? [Axoy]

The number of isomers of the C_{60}H_{3}
Buckminsterfullerene soccerball-shaped molecule. [Beedassy]

Smallest prime Fermat near miss, namely z such that x^3 + y^3 = z^3 - 1 (x less than y, y less than z). [Post]

The largest prime on the cover of Marcus du Sautoy's book "The Music of the Primes" (American Edition).

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]

There are 577 prime-digit primes (other than 577) less than a million. [Merickel]

The only 3-digit prime p such that 3p^3 contains three consecutive zeros in its decimal representation, i.e., 3*577^3=576300099. [Loungrides]

The solution to x^{2} - 2y^{2} = 1, where y
= 408. [Baudhayana]

A prime ruler can be purchased at Kyoto University for 577 yen.

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]