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Can someone check if I answered these two questions correctly:

  1. An unanswered question is whether there are infinitely many primes that are $1$ more than a power of $2$, such as $5=2^2+1$. Find two more of these primes: $$4^2+1=17, 6^2+1=37$$
  2. A more general conjecture is that there exist infinitely many primes of the form $n^2+1$. Exhibit five more primes of this type: $$10^2+1=101, 14^2+1=197, 20^2+1=401, 24^2+1=577, 26^2+1=677$$
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    $\begingroup$ $6$ is not a power of $2$. $\endgroup$ – user61527 Mar 13 '14 at 23:29
  • $\begingroup$ my bad so 16^2+1=257 $\endgroup$ – Lil Mar 13 '14 at 23:30
  • $\begingroup$ Yes, $16^2+1$ is good. $\endgroup$ – Daniel Fischer Mar 13 '14 at 23:31
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I don't think you have understood what the first question was asking, infinitely many primes of form 1 more than power of 2, i.e. $ 2^k + 1 = p$, not $ k^2 + 1$.

16 does work, but i just felt that perhaps you didn't understand what was being asked.

the 6 example would be a correct answer to the second question though. =P

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