Find the unit digit of the product of all the prime numbers in the series 1^1, 2^2........ till (13)^1302135

The unit digit of the product of all the prime numbers in the series 1^1, 2^2, 3^3, ..., 13^1302135 can be found by first identifying the prime numbers in the series and then finding the unit digit of each of these prime numbers raised to its respective power.

The prime numbers in the series are 2, 3, 5, 7, 11, and 13.

1. The unit digit of 2^2 is 4.
2. The unit digit of 3^3 is 7.
3. The unit digit of 5^5 is 5.
4. The unit digit of 7^7 is 3.
5. The unit digit of 11^11 is 1.
6. The unit digit of 13^1302135 is 3.

The product of these unit digits is 47531*3 = 1260.

The unit digit of 1260 is 0.

So, the unit digit of the product of all the prime numbers in the series 1^1, 2^2, ..., 13^1302135 is 0.