Greenwood's Conjecture
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Famous False Conjecture
Let $p$ be a prime number.
Let $T_p$ be the $p$th triangular number.
The conjecture states that:
Refutation
We have that $T_{31} = 496$, but $497 = 7 \times 71$ and so is not prime.
Historical Note
Greenwood's Conjecture was apparently made by a mathematician named Thomas Greenwood, but no information about him has yet been found on the internet.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $496$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $496$