Some primes are 1 more than a square. For example, 5 = 2 ² + 1. Can you find any other primes p so that p = n ² + 1? A) 2, 5, 7, ... B) 3, 4, 17, ... C) 13, 17, 65,... D) 3, 7, 17,... E) 5, 17, 37, ...

Question

Quizplus · Accepted Answer

There are infinitely many primes in the form $n^2+1$, and each of these primes can be expressed as $n^2+1=n(1)+1$, which fits the given form of $p=n(1)S_1U_1P_{12}S_1S_1P_0+1$. Therefore, the primes in this form include 5, 17, 37, and many more. The other answer choices do not necessarily contain primes in the specified form.

Some Primes Are 1 More Than a Square