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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest Wieferich prime: 1093^{2} divides 2^{1093  1}  1. In the opening scenes of the 1974 film "The Sugarland Express," a roadside signboard includes a marker for Texas Highway 1093. [Haga] The prime number 1093 equals 3^6+3^5+3^4+3^3+3^2+3+1 or the repunit 1111111 in base 3. [Dobb] 1093 = sigma(1^{0}) * sigma(9^{3}). [Firoozbakht] Thomas A. Edison (18471931) held 1093 successful U.S. patent applications. [Dobb] A Wieferich prime whose reversal is a brilliant number: 3901 = 47 * 83. [Post] 1093 divides every number of the form 3^(n!)1, for n>6. [Galliani] The addition at the end to 1093 of its third digit (from left), nine, produces 10939, which is prime. The same thing happens with the greater of the Wieferich primes, 3511. In fact, the addition at the end of one, which is the third digit of 3511 from left, produces 35111, which is prime. [Galliani]
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