# 510,510 is Product of 4 Consecutive Fibonacci Numbers

## Theorem

$510 \, 510$ Can be expressed as the product of $4$ distinct Fibonacci numbers:

$510 \, 510 = 13 \times 21 \times 34 \times 55$

and is also the $7$th primorial:

$510 \, 510 = 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17$

## Proof

By observation:

 $\ds 510 \, 510$ $=$ $\ds 13 \times 21 \times 34 \times 55$ $\ds$ $=$ $\ds 13 \times \paren {3 \times 7} \times \paren ({2 \times 17} \times \paren {5 \times 11}$ $\ds$ $=$ $\ds 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17$

$\blacksquare$

## Historical Note

David Wells report in his $1997$ work Curious and Interesting Numbers, 2nd ed. that this result can be found in an article by Monte James Zerger in Journal of Recreational Mathematics volume $12$, but this has not been corroborated.