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(another Prime Pages' Curiosity)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ There are 80 four-digit primes which are concatenations of two-digit primes. [De Geest]

+ (1080 - 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 two-digit 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 non-trivial 8-tuple. [Merickel]

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