17 has a representation as a sum of two squares: 17 = 12 + 42.
17 is the smallest number with four representations as a sum of three primes: 17 = 2 + 2 + 13 = 3 + 3 + 11 = 3 + 7 + 7 = 5 + 5 + 7.
17 and 19 form a twin prime pair.
17 is the hypotenuse of a primitive Pythagorean triple: 172 = 82 + 152.
17 is the first sum of two distinct fourth powers: 17 = 14 + 24.
There are 17 ways to express 17 as the sum of one or more primes; 17 is the only integer that is equal to the number of prime partitions of itself.
17 is the first sum of two distinct fourth powers: 17 = 14 + 24.
There are 17 ways to express 17 as the sum of one or more primes; 17 is the only integer that is equal to the number of prime partitions of itself.
Carl Friedrich Gauss proved at the age of 18 that one can construct a regular polygon with a prime number of sides with the use of only straight edge and compasses only if the number of sides is of the form 22^n. Hence, one can construct a regular 17-gon with rule and compasses only.
Source: Number Gossip
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