# 169

This number is a composite.

169 = (2^{7} + 7^{2}) - (7 + 1) and is the smallest perfect square of the form
(2^{p} + *p*^{2}) - (*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]

169^100-168^99 is the smallest prime of form x^100-(x-1)^99. Note that 10099 is also prime and 169+168 is an 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]

If A = 1, B = 2, C = 3, … , Z = 26, then PETER WALLRODT is "brilliant," just like M^2. [Worrom]