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This is a modular equation involving first $k$ ODD primes:

$$ 3^{5+7+11+13+17+\dotsb+p(k-3)+p(k-2)}=p(k-1) \mod p(k) $$

where $p(k)$ is the $k$-th ODD prime number.

I've checked $k$ up to $50$, but the only solution I've found is for $k=20$.

Are there any other solutions for $k$?

Mike Pierce
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Pink Dolphin
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  • Why did you stop at $k=50$? This doesn't seem to require too much computational power. You could easily go up to $10$ billion. – barak manos Feb 15 '15 at 17:42

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