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While experimenting, I found that every number up to $200000$, with the sole exception of $216$ is the sum of a prime and a triangular number (where $0$ and $1$ are included as prime). Is anything known about this?

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    Why are $0$ and $1$ included as prime? They are not prime.2012-10-10
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    Yes: http://arxiv.org/abs/0803.3737 Also [oeis](http://oeis.org/search?q=sum+of+prime+and+triangular+number&language=english&go=Search) has something2012-10-10
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    Should be reformulated as: is the sum of triagular and prime or is triangular or is triangular +1. Checking only up to 200000 and already finding one counterexample seems not very promising to me.2012-10-10
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    Confirmed up to 10 million with the only exception being 216 (as stated by the OP)2012-10-10
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    @E.O. Did you happen to check up to higher numbers?2016-11-26

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