# A number theory problem by Anthony Pham

**Number Theory**Level pending

There is a special six-digit number *n* such that:

-its first two digits(*a*), its middle two digits(*b*), and its last two digits(*c*) each form a two-digit prime number

-*a*<*b*<*c*

-*c* is greater than a by 60

-the units digits of *b* is 3

-it has three two-digit prime factors, which if written out from least to greatest, it is greater than *n* by 100000

What is the six-digit number *n*?