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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 126*126!_{8} + 1 is prime. [Fougeron] The smallest multidigit number such that the sum of its prime factors (without repetition) equals the product of its digits. [Russo] 126 multiplied by the 126th Lucas number plus and minus one results in twin primes of prime length (29 digits). This is the largest such Lucas number less than 10^2000. [Opao] 126^126 + 126! + 126*126 + 126/126 + 126 is prime. It is interesting that the digits of 126 have the same property. [Firoozbakht] The prime gap that covers the first century with no primes (from 1671800 to 1671899) has length 126 (from 1671781 to 1671907). 126!  126*126  126/126 is a 212digit prime. [Firoozbakht]
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