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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The first three digits in the decimal expansion of the EulerMascheroni 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 soccerballshaped 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 3digit 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 primedigit primes (other than 577) less than a million. [Merickel] The only 3digit 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.
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