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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The largest known natural number n such that n  3^{k}, with n > 3^{k}, is prime for all k > 0. [Capelle] 1330 is the only number m less than 7777777 such that m  3^k is prime for k = 1, 2, . . . , 9. [Firoozbakht] 1330 begins the first decade of numbers, 10n through 10n + 9, where n is a nonnegative integer, in which 10n + 5 is divisible by 3 and there are no primes. [Litman] There are 1330 sphenic numbers whose the prime factors are doubledigit primes. May we call them “2sphenic numbers”? [Loungrides]
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