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222 is the smallest number n such that 3 + n, (3*5) + n, (3*5*17) + n, (3*5*17*257) + n, (3*5*17*257*65537) + n are all primes. Note that 3, 5, 17, 257 and 65537 are the known Fermat primes, with the property (F0*F1*F2*...*Fn-1) + 2 = Fn [Capelle]

 

  Submitted: 2007-12-23 09:02:18;   Last Modified: 2008-01-30 11:28:00.



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