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How we can find a 5-digits number $q$ such that $2^q+17$ be a prime number? Does there exist such number?

Mankind
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SKMohammadi
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  • from where does this problem come? – Dr. Sonnhard Graubner Mar 23 '16 at 17:43
  • I do not know. Someone asked me :) – SKMohammadi Mar 23 '16 at 20:49
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    Honestly, you find it by testing every $5$-digit number until you find one that gives a prime. You can sieve out some based on divisibility by small primes (e.g. if $q$ is even then $2^q+17$ is a multiple of $3$), but you'll still probably have to check many hundreds of cases by computer. Why don't you ask "someone" to find a $5$-digit $q$ such that $2^q + 78557$ is prime? :) – Erick Wong Mar 23 '16 at 21:23
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    The only such number is 77121. Thank Neal Sloane, Robert Wilson and Robert Price for the answer. http://oeis.org/A057200 – David R. Mar 23 '16 at 21:30

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