Sum of 714 and 715

Theorem

The sum of $714$ and $715$ is a $4$-digit integer which has $6$ anagrams which are prime.

Proof

We have that:

$714 + 715 = 1429$

Hence we investigate its anagrams.

We bother only to check those which do not end in either $2$ or $4$, as those are even.

\(\ds 1429\)

\(\)

\(\ds \)

is prime

\(\ds 1249\)

\(\)

\(\ds \)

is prime

\(\ds 4129\)

\(\)

\(\ds \)

is prime

\(\ds 4219\)

\(\)

\(\ds \)

is prime

\(\ds 2149\)

\(=\)

\(\ds 7 \times 307\)

and so is not prime

\(\ds 2419\)

\(=\)

\(\ds 41 \times 59\)

and so is not prime

\(\ds 9241\)

\(\)

\(\ds \)

is prime

\(\ds 9421\)

\(\)

\(\ds \)

is prime

\(\ds 2941\)

\(=\)

\(\ds 17 \times 173\)

and so is not prime

\(\ds 2491\)

\(=\)

\(\ds 47 \times 53\)

and so is not prime

\(\ds 4291\)

\(=\)

\(\ds 7 \times 613\)

and so is not prime

\(\ds 4921\)

\(=\)

\(\ds 7 \times 19 \times 37\)

and so is not prime

Of the above, $6$ are seen to be prime.

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $714$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $714$