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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The first Human Genome Project online download contained a 739 megabyte file. The smallest prime number that is the sum of distinct primes beginning and ending with the digit three (739 = 3 + 353 + 383). [Capelle] The smallest prime (emirp) that can be expressed as a sum of powers with the four prime digits as bases and exponents, i.e., (2^7+3^5+5^2+7^3). [Loungrides] The smallest emirp that has a maximum product of digits for a prime sum of digits. [Loungrides] The start of five consecutive emirps in the sequence of Ulam primes, i.e., 739, 751, 983, 991, 1103. [Loungrides] The smallest prime number that has both no digits in common with its square and the same sum of digits as its square. [Gaydos] 7^39 is a 33digit number without a 7 in it. Can you find a larger power of 7 without the digit 7 in it? [Loungrides] 739 is the largest prime used in Jean Brette's 31digit approximation for : ln[(2^5*5#*23*29)^3+739+5]/sqrt(163) = 3.141592653589793238462643383279... . [Rivera] 739 is at the end of a conveyor belt on the cover of "The Prime Number Conspiracy: Biggest Ideas in Math from Quanta."
(There are 3 curios for this number that have not yet been approved by an editor.)
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