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?

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