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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) There are 80 fourdigit primes which are concatenations of twodigit primes. [De Geest] (10^{80}  80)/80 is prime. [Luhn] 80^(80+1) + (80+1)^80 is prime. The largest natural number n such that all prime factors of n and n+1 are smaller or equal to the prime digit 5. [Capelle] The only twodigit integer n that yields a prime in the form n^(n+1)+(n+1)^n. [Silva] The smallest integer n such that both n and n+1 are products of at least 4 primes. [Post] Theoretically, the fewest prime factors in the numbers spanning a nontrivial 8tuple. [Merickel]
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