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(just those submitted by Firoozbakht)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

Just showing those entries submitted by 'Firoozbakht': (Click here to show all)

+ (8^8+88888)/8 is prime. Note that eight 8s are used. [Firoozbakht]

+ (pi(0)! + pi(1)! + ... + pi(k)!) is prime only for k = 1,2,..,8 (composite for k>8). [Firoozbakht]

+ For n > 8, prime(n) > pi(n) + sigma(n), so 8 is the only number n such that prime(n) = pi(n) + sigma(n). [Firoozbakht]

(There is one curio for this number that has not yet been approved by an editor.)




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