# 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): $496$