The book is now available! 169
(another Prime Pages' Curiosity)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ 169 = (27 + 72) - (7 + 1) and is the smallest perfect square of the form (2p + p2) - (p + 1). [Charles]

+ The smallest square that is prime when turned upside down. [Wu]

+ 169 is the first composite Pell number with a prime index. Coincidentally, it is also the last square in the Pell sequence. [Axoy]

+ The sum of first 12 powers of semiprimes is (12+1)^2. [Post]

+ The sum of first five emirps can be represented as the square of the first emirp. [Loungrides]

+ The lucky numbers of Euler are well known. But what will happen if we change the formula a little? Consider A = 169 - n - n^2. The expression A is prime for n = 1 to 12 and |A| is prime for n = 1 to 24. Do you know another number which give the same results except 4, 9, 25 and 49? [Petrov]

+ The smallest square such that every digit (d) repeated d times gives prime. Note that the same is true if we reverse or invert the digits of the number 169, i.e. 1666666999999999, 9999999996666661 and 6666669999999991 are all primes. [Petrov]

(There are 4 curios for this number that have not yet been approved by an editor.)




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