Prime Curios!: 400

400
(another Prime Pages' Curiosity)

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400 is the smallest number m such that |m^k -prime(m)| for k = 1,2,...,5 are primes. [Firoozbakht]

(400/004)! + prime(400) is prime. [Firoozbakht]

400 is the only known square of the form 1+p+p^2+p^3, where p is prime or composite. (Note that p=1 yields a square, but 1 is neither prime nor composite.) [Noe]

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

To link to this page use http://primes.utm.edu/curios/page.php?number_id=4334