I tried to solve this equation: $$3^{5+7+11+13+...+P(k-3)+P(k-2)}=P(k-1) \mod [ P(k) ],$$ where P(k) here is the $k^{th}$ odd prime number. The only solution I have found is $k=52$ or $P(k)=241$. Could you find the next solutions for $k$?
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what are odd primes? – Math-fun Feb 19 '15 at 21:28
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Odd primes are 3,5,7,11,13,17,19,23,29,31,37,41,.... – Tanaka C Feb 19 '15 at 21:29
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Many thanks for the quick reply. Sorry for asking, this is just for me to learn: Are there even primes too? – Math-fun Feb 19 '15 at 21:35
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@Mehdi,no,even prime is excluded here. – Tanaka C Feb 19 '15 at 21:36
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@Mehdi Yes, 2 is even and prime! – Fermat Feb 19 '15 at 21:40
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@Fermat that is true! thanks, I just realized. never paid attention to this. – Math-fun Feb 19 '15 at 21:42