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# Prime Numbers

2, 3, 5, 7, ... The set of prime numbers is the alphabet of mathematics that allows us to communicate across the universe.

# Prime Numbers: Level 3 Challenges

$2^{2014}+ 1007^4$ Is this sum equal to a prime number?

Mr. White is an approximately forty years old father with 4 sons of distinct ages. Writing his age 3 times in succession, we get a 6-digit number that is equal to the product of his age, his wife's age and his 4 sons' ages.

Give the sum of his wife's age and all 4 sons' ages.

A three-digit number $$N$$ has first digit $$a (\neq 0)$$, second digit $$b$$ and third digit $$c$$. $$N = b(10c + b)$$ where $$b$$ and $$(10c + b)$$ are primes. Find $$N$$.

How many integers from $$1$$ to $$100$$ inclusive can be written as the product of two (not necessarily distinct) primes?

If you can find a computer science or combinatorics approach, post your solution!

What is the last digit of the largest prime number?

See Part 1, and Part 3.

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