# 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 C60H3 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] 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]

(There is one curio for this number that has not yet been approved by an editor.)