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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest fourdigit zeroless prime such that 2+267, 22+67, and 226+7 are also distinct primes. [Opao] 2267 is the sum of the squares of three distinct primes (3^2 + 7^2 + 47^2). [Suzuki] The only prime less than a googol of form p^a(q^b+r^c) where (p, q, r) are three successive primes p > q > r and a, b, c their orders, i.e., 7^4(5^3+3^2). [Loungrides] (2267, 2269) is the first pair of twin primes of form (n*R(n)1, n*R(n)+1), case n=36. Can you find the next one such pair? [Loungrides]
(There is one curio for this number that has not yet been approved by an editor.)
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