prime number greater than 10 to the 15th?

Answer 1

The "Top Ten" Record Primes are here
http://primes.utm.edu/largest.html
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Answer 2

On the page below, one of Chris Caldwell's Prime Pages, there is a list of ten primes of 20 digits each, ten of 30 digits, and so on up to 100 digits. The next page (small2.html) lists primes of 110 to 200 digits, and the following page (small3.html) primes of 210 to 300 digits.

With modern algorithms, it is really quite easy to generate and test primes of these sizes on a typical PC, and primes of up to 500 or 600 digits on more powerful machines.