# Chaitanya's Random Pages

## September 23, 2012

### 7^7 – 6^6

Filed under: mathematics — ckrao @ 11:07 am

I didn’t expect this number to be so memorable.

### $\displaystyle 7^7 - 6^6 = 776,887$

• It starts and ends with the digit 7.
• It has only 3 different digits (consecutive ones at that and including 6 and 7).
• The first three digits of the number are the same as the first three digits of the original expression $7^7 - 6^6$. They are also easy to recall if you link it to when the ancient Olympics were first held or when the US Declaration of Independence was signed. (I often link numbers to years of events as a memory aid.)
• The two three-digit numbers 776 and 887 making up the six-digit number differ by 111. 🙂

For what it’s worth the result also happens to be prime.