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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest prime that may be written as 2a^{2}  1, and also as 3b^{3}  1. [Hartley] A man described as looking like a plump Moses asked the following questions during a 1987 joint American Mathematical Society/Mathematical Association of America conference in San Antonio, Texas: "What about 647? Is it prime?" (from The Man Who Loved Only Numbers by Paul Hoffman) 647 equals the sum of all twodigit even semiprimes plus one. [Silva] The largest prime whose digits form an acuteangle scalene triangle with prime perimeter. [Loungrides] The largest 3digit number n such that 3^n2^n is prime, 3^6472^647. [Loungrides] The only prime of form p^(p+1)+q^(q+1)1, where p, q are consecutive primes, i.e., 2^3*3^41. [Loungrides]
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