# Not a "Coincidence" Again!

**Number Theory**Level 5

\[ 0. \,\ 029 \,\ 031 \,\ 037 \,\ 047 \,\ 061 \,\ 079 \,\ 101 \,\ 127 \,\ 157 \dots \]

Above shows the first few digits decimal expansion of \(\large{\frac{28944031}{997002999}}\), written in groups of 3.

If we split this decimal expansion into groups of 3 we see multiple primes appearing! However these primes end at a certain point. After how many decimal (digits) does this pattern cease?

**Details and Assumptions**:

- If you think the number equals to \( 0.\ 029 \,\ 031 \,\ 037 \,\ 047 \,\ 063 \), then you can only find the five prime numbers. So we can only find 4 positive prime numbers before the pattern breaks off. Thus the pattern breaks off after 12 decimal digits.

Inspired by Garret C., Pi Han Goh and Daniel Liu.