66 = 2 x 3 x 11
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409,457 = 71 x 73 x 79
2 x 3 x 3 x 7 = 126 =2*7*3*3
Yes it is called the fundamental theorem of arithmeticand it says that every whole number greater than one, the natural numbers, can be written as a unique product of primes. Dr. Chuck Mathdoc
sqrt 66 = sqrt (2 x 3 x 11) = sqrt 2 x sqrt 3 x sqrt 11. All of these are irrational so their product is also.
16 = 1+15, 3+13, 5+11, 7+92,3,5,7,11,13 are primes < 1616 = 3+13 or 5+11